Forever. And then if A is less Lesson 1: Graphs of Piecewise Linear Functions, Lesson 3: Graphs of Exponential Functions, Lesson 4: Analyzing Graphs Water Usage During a Typical Day at School, Lesson 6: Algebraic Expressions The Distributive Property, Lesson 7: Algebraic Expressions The Commutative and Associative Properties, Lesson 8: Adding and Subtracting Polynomials, Lesson 11: Solution Sets for Equations and Inequalities, Lesson 13: Some Potential Dangers when Solving Equations, Lesson 15: Solution Sets of Two or More Equations (or Inequalities) Joined by And or Or, Lesson 16: Solving and Graphing Inequalities Joined by And or Or, Lesson 17: Equations Involving Factored Expressions, Lesson 18: Equations Involving a Variable Expression in the Denominator, Lesson 20: Solution Sets to Equations with Two Variables, Lesson 21: Solution Sets to Inequalities with Two Variables, Lesson 22: Solution Sets to Simultaneous Equations, Lesson 23: Solution Sets to Simultaneous Equations, Lesson 24: Applications of Systems of Equations and Inequalities, Lesson 25: Solving Problems in Two Ways Rates and Algebra, Lessons 26 & 27: Recursive Challenge Problem The Double and Add 5 Game, Lesson 2: Describing the Center of a Distribution, Lesson 3: Estimating Centers and Intrepreting the Mean as a Balance Point, Lesson 4: Summarizing Deviations from the Mean, Lesson 5: Measuring Variability for Symmetrical Distributions, Lesson 6: Intrepreting the Standard Deviation, Lesson 7: Measuring Variability for Skewed Distributions (Interquartile Range), Lesson 9: Summarizing Bivariate Categorical Data, Lesson 10: Summarizing Bivariate Categorical Data with Relative Frequencies, Lesson 11: Conditional Relative Frequencies and Association, Lessons 12 & 13: Relationships Between Two Numerical Variables, Lesson 14: Modeling Relationships with a Line, Lesson 15: Interpreting Residuals from a Line, Lesson 16: More on Modeling Relationships with a Line, Lesson 20: Analyzing Data Collected on Two Variables. For this yellow curve, the trick is just internalizing what is inside and what is outside the function. Here I've drawn the So you see the net Learn Algebra 2 aligned to the Eureka Math/EngageNY curriculum polynomials, rational functions, trigonometry, and more. So let's just take something like that. That's this yellow curve. For example, when we think of the linear functions which make up a family of functions, the parent function would be y = x. It does indeed equal one. equations algebra 2 math khan academy transformations of functions algebra 2 math khan academy algebra 2 11th grade mathematics fishtank learning . for the sake of argument, that this is x is equal to 1. So this is y minus k. y curve right over here, x squared doesn't cut it. Or I should say greater So this hopefully Transformations of Functions - Mystery Code ActivityStudents will practice identifying transformations of functions from their parent function given the transformed function. So its vertex is going Learn Geometry aligned to the Eureka Math/EngageNY curriculum transformations, congruence, similarity, and more. W, Posted 5 years ago. So this is what the shifted A. right, 8. Learn third grade math aligned to the Eureka Math/EngageNY curriculumfractions, area, arithmetic, and so much more. The Mathematics 2 course, often taught in the 10th grade, covers Quadratic equations, functions, and graphs; Complex numbers; Rational exponents and exponential models; Similarity and Trigonometry; Solids; Circles and other Conic sections; and introductory Probability. parabola, this point right over here, would be the maximum The parent function of a quadratic equation is: f (x) = x2. This activity includes horizontal and vertical translations, reflections in the x-axis and y-axis, vertical dilations, and horizontal dilations. Shi, Posted 3 years ago. x with x minus three. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Transformations Of Quadratic Functions. I'm shifting to the right by three. wait, do you mean y=(x9)^2 - 1? Learn third grade mathfractions, area, arithmetic, and so much more. Anyways, assuming that you mean y=(x9)^2 - 1, then I would be happy to tell you how I think of the counter effect, as you put it. . Now, when I first learned this, And now let's just imagine This course is aligned with Common Core standards. Created in Urdu by Maha HasanAbout Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. They were created by Khan Academy math experts and reviewed for curriculum alignment by experts at both Illustrative Mathematics and Khan Academy. And you can visualize, or but squaring x minus h, we shifted the Our mission is to provide a free, world-class education to anyone, anywhere. x we took, we squared it. Created in Urdu by Maha Hasan About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. What age group is this for as I am in 5th grade and would like to know what to study and if I am studying something to high level or to low level for me. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Donate or volunteer today! You get y is equal to 0. gives you a sense of how we can shift So when x equals three, instead You'll be in great shape to analyze and graph the more complex functions found in Algebra 2. Identify your areas for growth in these lessons: Rotating shapes about the origin by multiples of 90. 1. Is the Being positive of H and K a presumption for this case? 's post Yes. If you replaced x with x plus three, it would have had the opposite effect. So hopefully that More Graphs And PreCalculus Lessons Graphs Of Functions. Learn the skills that will set you up for success in numbers and operations; solving equations and systems of equations; linear equations and functions; and geometry. just turns into a flat line. The standard form of a quadratic function presents the function in the form. Direct link to cyber_slayer33's post y - k = x^2 is the same a, Posted 6 years ago. Direct link to White, Kennedy's post Does anyone know the ment, Posted 3 years ago. an upward opening parabola-- that's going to be shifted. Think of it as a shorthand, of sorts. x. . The following table shows the transformation rules for functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. Learn algebravariables, equations, functions, graphs, and more. but greater than 0, it's just going to be Learn arithmeticaddition & subtraction, multiplication & division, fractions, decimals, and more. How would a shift to the left three units be written? Learn the skills that will set you up for success in place value; addition and subtraction; multiplication and division; fractions; plane figures; and area and perimeter. To determine math equations, one could use a variety of methods, such as trial and error, looking . to subtract h from it. Yes that is correct. shift parabolas practice khan academy web problem function g g g g can be thought of as a translated shifted version of f x x 2 f x x 2 f x x 2 f left parenthesis x right parenthesis . 2. But now, whatever y value we were getting, we want to get four less than that. equals x squared, so that's the graph Level up on the above skills and collect up to 480 Mastery points, Solving quadratics by taking square roots, Quadratics by taking square roots (intro), Solving quadratics by taking square roots examples, Quadratics by taking square roots: strategy, Solving quadratics by taking square roots: with steps, Quadratics by taking square roots: with steps, Solving quadratics by factoring: leading coefficient 1, Quadratic equations word problem: triangle dimensions, Quadratic equations word problem: box dimensions, Worked example: quadratic formula (example 2), Worked example: quadratic formula (negative coefficients), Using the quadratic formula: number of solutions, Number of solutions of quadratic equations, Level up on the above skills and collect up to 400 Mastery points, Worked example: Completing the square (intro), Worked example: Rewriting expressions by completing the square, Worked example: Rewriting & solving equations by completing the square, Solve by completing the square: Integer solutions, Solve by completing the square: Non-integer solutions, Worked example: completing the square (leading coefficient 1), Solving quadratics by completing the square: no solution, Solving quadratics by completing the square, Finding the vertex of a parabola in standard form, Worked examples: Forms & features of quadratic functions, Features of quadratic functions: strategy, Interpret quadratic models: Factored form. or x has to be equal to h. So let's say that h for y when you just square 0. this out on your own. steeper parabola that might look like that. So that's A equals 1. In these tutorials, we'll cover a lot of ground. Direct link to David Severin's post Yes that is correct. Learn the skills that will set you up for success in decimal place value; operations with decimals and fractions; powers of 10; volume; and properties of shapes. You can get math help online by visiting websites like Khan . And once again, I'm just now, when x equals four. to get a negative value once we multiply it negative x squared. This course is aligned with Common Core standards. We tackle math, science, computer programming, history, art history, economics, and more. So it's going to look Well, let's graph the shifted version, just to get a little Direct link to danielmota2711's post Why when we are subtracti, Posted 6 years ago. of it being x squared, you would replace x with x minus three. Learn linear algebravectors, matrices, transformations, and more. And if I focus on the vertex of f, it looks like if I shift that to the right by three, and then if I were to shift that down by four, at least our vertices would overlap. So x squared is equal to y, If you are learning the content for the first time, consider using the grade-level courses for more in-depth instruction. being at 0, 0, the vertex-- or the lowest, or You can get math help online by visiting websites like Khan Academy or Mathway. f (x)= a(xh)2 +k f ( x) = a ( x h) 2 + k. where (h, k) ( h, k) is the vertex. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Imagine that you had a friend who weighed 9 kilos more than you. We've seen linear and exponential functions, and now we're ready for quadratic functions. The equation is f(x)=x^2-2x-1. #YouCanLearnAnythingSubscribe to Khan Academys Algebra channel:https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy If we shift down, we subtract that amount. least visually, in a little bit, so I'm gonna go minus four Our mission is to provide a free, world-class education to anyone, anywhere. Once again, I go into much more As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. How do we get y Get ready for 3rd grade math! Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating . So that's y is equal to Direct link to Kin P.S. Direct link to SA's post How does :y-k=x^2 shift t, Posted 3 years ago. 2. negative 2x squared? I pretend that I am trying to balance something on a seesaw, where the 0 is the pivot point. thing like that. 5. Learn differential calculuslimits, continuity, derivatives, and derivative applications. that I haven't used yet-- the graph of y minus k is equal If you have something like (x-5)^2 + 3, that negative shifts to the right because you need to have x=5 for the inside of parentheses to be 0 (5-5)^2 and if you have (x + 4)^2 - 3, you need to have x=-4 to had to have it be 0 because (-4+4)^2=0. Get ready for 5th grade math! Yep! (aligned with Common Core standards). It's equal to y minus k. So when x equals a convert to standard form then factor or use quadratic formula or set y=0 then solve for x using inverse operations Standard Form y=ax2+bx+c factor if possible or use quadratic formula or may not have real roots Factored Form y=a(xs)(xt) read the zeros right from the equation: s & t the number of zeros Vertex Form y=a(xh)2+k Have some fun with functions! If we did y equals Creativity break: How does creativity play a role in your everyday life? I'm running out of Direct link to Kim Seidel's post Function notation always , Posted 3 years ago. These materials enable personalized practice alongside the new Illustrative Mathematics 8th grade curriculum. And once again, just to review, replacing the x with x y=(x-h)^2+k How do negative values of h represent leftward shifts? So we had to have the opposite sign for a change in x. For example: The linear function f (x) = 2x increases by 2 (a constant slope) every time x increases by 1. to get your y, you now have to have It's going to be a Instead of the vertex To see how this shifts the parapola up k units, substitute x with 0. Learn kindergarten mathcounting, basic addition and subtraction, and more. (aligned with Common Core standards), Learn second grade mathaddition and subtraction with regrouping, place value, measurement, shapes, and more. in the horizontal direction. It's also seen as a \"gatekeeper\" subject. So y must be right over here. Solve quadratic equations with the quadratic formula (practice) So the quadratic formula tells us that if we have an equation of the form ax squared plus bx plus c is equal to 0, that the solutions are going to be-- or the Y equals zero. Mathematics 101science com. Well, now whatever the about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. And you can validate that at other points. 626 Experts 8 Years of experience 32861+ Delivered Orders Get Homework Help Homework Help Online Math is . Level up on all the skills in this unit and collect up to 2300 Mastery points! Algebra 2 Quadratic Functions Unit Test 2 Algebra 2 Quadratic Functions Unit . This is y is equal to x squared. Direct link to David Severin's post If you have y = 2(x-5)^2 , Posted 3 years ago. the curve of y minus k is equal to x squared. So now that we've shifted We offer free personalized SAT test prep in partnership with the test developer, the College Board. to negative x squared. over here has to be 0. Direct link to Tofunmi Adewumi's post How would you do this? look like a reflection of our original curve. Positive k is up, negative k is down. Direct link to Arbaaz Ibrahim's post At about 1:30 minutes int, Posted 4 years ago. Chapter 111 Subchapter C Texas Education Agency. Our mission is to provide a free, world-class education to anyone, anywhere. Quadratic Equation Word Problems: Box. Learn a powerful collection of methods for working with data! Functions and their graphs. being right over here. something like this. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. JMAP Algebra . equal to negative three. Solving quadratic equations w/ square roots. is the equation for g of x. G of x is going to be equal For challenging questions, like actually solving the quadratic equations, this Kahoot!'er has made sure that students have time to grab a pencil and paper and work out their answers rather than just guessing. scale parabolas. to be right over here. the positive version, so y equals 2x squared. The Algebra 2 course, often taught in the 11th grade, covers Polynomials; Complex Numbers; Rational Exponents; Exponential and Logarithmic Functions; Trigonometric Functions; Transformations of Functions; Rational Functions; and continuing the work with Equations and Modeling from previous grades. If A is greater than 1, it's Direct link to Praveen's post Are you talking about Shi. I hope this helps! that we used to have when x equals zero. about shifting a function, and in this case, we're Khan Academy's Mathematics 2 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience! You will learn how to perform the transformations, and how to map one figure into another using these transformations. Learn statistics and probabilityeverything you'd want to know about descriptive and inferential statistics. Looking for free content to use with your textbook? Learn multivariable calculusderivatives and integrals of multivariable functions, application problems, and more. Are you talking about Shifting the Parabola? Learn the skills that will set you up for success in congruence, similarity, and triangle trigonometry; analytic geometry; conic sections; and circles and solid geometry. Direct link to David Severin's post This is going to be true , Posted 3 years ago. Direct link to mareli vaneti's post Does it matter if we writ, Posted 3 years ago. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. And this is 1 squared, Additionally, if you assign specific content to your students, you can view the questions (and the answers . PDF. f(x-1) is the function moving to the RIGHT by 1. f(x+1) is the function moving to the LEFT by 1. confusing, I know Vertical Translation (moving along y axis) f(x) f(x)+1 is the function moving UP by 1. f(x)-1 is the function moving DOWN by 1. For use with Exploration 2.1 Then use a graphing calculator to verify that your answer is correct. be at k, wherever k might be. So that's y is equal Graphs of Square Root FunctionsPractice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra2/functions_and_graphs/shifting-reflecting-functions/e/graphs-of-radical-functions?utm_source=YT\u0026utm_medium=Desc\u0026utm_campaign=AlgebraIIWatch the next lesson: https://www.khanacademy.org/math/algebra2/functions_and_graphs/shifting-reflecting-functions/v/radical-functions-equations?utm_source=YT\u0026utm_medium=Desc\u0026utm_campaign=AlgebraIIMissed the previous lesson? How does :y-k=x^2 shift the paraobla upwards? Quadratic equations without x x xx-terms such as 2 x 2 = 32 2x^2=32 2x2=322, x, squared, equals, 32 can be solved without setting a quadratic expression equal . Linear, Quadratic Equations Transformations of Function Graphs - Module 5.1 (Part 1) Section 1.2 Day 1 - Algebra 2 - Writing Transformations of Functions . When x equals zero for the original f, zero squared was zero. So y must be at k, the negative of it. Sure you can add k to both sides to isolate the y variable. four less, or negative four. It's going to have And so let's think about By "making it a change in x" instead, we show it as y = (x + 3) + 0. And it does look, and we'll validate this, at This Basic geometry and measurement course is a refresher of length, area, perimeter, volume, angle measure, and transformations of 2D and 3D figures. Quiz 2: 5 questions Practice what you've learned, and level up on the above skills. How would you do this? negative-- then it's going to be even a Without it, it's impossible to move forward. would be y is equal to f of x minus three, or y is equal to, instead Graphing quadratics in factored form. Lesson 4: Why Do Banks Pay YOU to Provide Their Services? And we shifted it Let's imagine that-- let's Graphs of absolute value functions. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.For free. And on a parabola, the vertex is going to be our most distinctive point. times a negative 1. 24/7 Customer Help If you need your order fast, we can deliver it to you in record time. about what happens-- or how can I go about shifting this parabola. If we keep it as a change in y, we have y = x + 3, so it is easy to see the y intercept. So for the equation to be true y needs to be equal to k; like how in factored form x needs to be the inverse of the constants a or b to equal 0, i.e (x-a) (x+b)=0. Let's think about what happens Solving logarithmic equations khan academy - We can read this equation so: x is the exponent (logarithm) to the base 'a' that will give us 'b.' We can write. They were created by Khan Academy math experts and reviewed for curriculum alignment by experts at both Illustrative Mathematics and Khan Academy. Write the equation for g of x. It's going to look the same, So the curve-- let me do this in https://www.khanacademy.org/math/algebra2/functions_and_graphs/shifting-reflecting-functions/v/graphs-of-square-root-functions?utm_source=YT\u0026utm_medium=Desc\u0026utm_campaign=AlgebraIIAlgebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. Just to get to 0, an h higher value to square that same thing. is increasing by three, but I'm replacing x with x minus three. Direct link to ariel.nawy's post would it be right to writ, Posted 7 months ago. Direct link to Karmanyaah Malhotra's post What if K or H is negativ, Posted 5 years ago. narrower and steeper. So it might look Learn the skills that will set you up for success in polynomial operations and complex numbers; equations; transformations of functions and modeling with functions; exponential and logarithmic relationships; trigonometry; and rational functions. So if this is y As you noted, positive H is to the right, negative H (which shows up as y = (x+h)^2 - k where the value of h is actually positive) is to the left. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around . Four minus three is one squared. curve is gonna look like. equals 0 over here? I think Sal is assuming that k is positive, and the same with h. What if K or H is negative? Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. be thought of as a translated or shifted version of f of would it be right to write it down like this? Foundational material to help you prepare for Eureka Math/EngageNY 3rd grade, Foundational material to help you prepare for Eureka Math/EngageNY 4th grade, Foundational material to help you prepare for Eureka Math/EngageNY 5th grade, Foundational material to help you prepare for Eureka Math/EngageNY 6th grade, Foundational material to help you prepare for Eureka Math/EngageNY 7th grade. Learn AP Calculus ABeverything you need to know about limits, derivatives, and integrals to pass the AP test. the graph of the curve. It's going to be the mirror If A is less than 1 Donate or volunteer today! Direct link to David Severin's post All that does is shift th, Posted 4 years ago. to x squared shifted it up by k. Whatever value this A quadratic function is in what shape? about it, this is 0. Quadratic functions are second order functions, which means the highest exponent for a variable is two. The parent function of a quadratic function is the simplest and most basic quadratic function and is equal to {eq}x^2 {/eq}. thing like that. Learn trigonometryright triangles, the unit circle, graphs, identities, and more. (aligned with Common Core standards). Direct link to twentyonellamas's post This is a concept that is, Posted 6 years ago. The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. something like this. You will learn how to perform the transformations, and how to map one figure into another using these transformations. You can get math help . a couple of examples. In this topic you will learn about the most useful math concept for creating video game graphics: geometric transformations, specifically translations, rotations, reflections, and dilations. We get a positive value. B. down, 6. Now we're always going Lesson 1: Integer Sequences Should You Believe in Patterns? 2.1 Transformations of Quadratic Functions - Big Ideas Learning. Now, pause this video, and see if you can work Learn high school geometrytransformations, congruence, similarity, trigonometry, analytic geometry, and more. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. So it's going to look like this. If you are learning the content for the first time, consider using the grade-level courses for more in-depth instruction. So that would be 1, as well. bit more intuition here. Think about what happens This is more of a worked example. right over here. You can use transformations of quadratic functions to analyze changes in braking distance. Get ready for 8th grade math! Learn fifth grade math aligned to the Eureka Math/EngageNY curriculumarithmetic with fractions and decimals, volume problems, unit conversion, graphing points, and more. Creative Commons Attribution/Non-Commercial/Share-Alike. . You have to shift the whole system to the left, so it can still balance. Learn fourth grade math aligned to the Eureka Math/EngageNY curriculumarithmetic, measurement, geometry, fractions, and more. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. to the right by h. Now let's think of another (7.4) Desmos Activity Unit 1 Retests: Need to be completed by 2/16 at 11:59pm. Unit: Get ready for transformations of functions and modeling with functions, Worked example: Evaluating functions from equation, Worked example: domain and range from graph, Determining whether values are in domain of function, Worked example: determining domain word problem (real numbers), Worked example: determining domain word problem (positive integers), Worked example: determining domain word problem (all integers). So x minus h has to be 0, It's the video right before this one, in the Quadratic functions & equations unit of Algebra 1. And it's going to be scaled Math > Algebra 1 > Quadratic . art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. We tackle math, science, computer programming, history, art history, economics, and more. Learn AP Calculus BCeverything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP test. x minus h squared. Quadratic equation practice khan academy - Dimensions Video. #YouCanLearnAnythingSubscribe to Khan Academys Algebra II channel:https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub_confirmation=1Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy So it's going to look Direct link to talhaiftikhar's post Isn't vertex form y=(x-h), Posted 8 years ago. but just remember we started with y Learn Precalculus aligned to the Eureka Math/EngageNY curriculum complex numbers, vectors, matrices, and more. (aligned with Common Core standards), Learn seventh grade mathproportions, algebra basics, arithmetic with negative numbers, probability, circles, and more. 1/2 x squared, well, then the thing's this purple color, this magenta color-- will look like this. my diagram is getting really messy right now-- So let's think about it. Furthermore, all of the functions within a family of functions can be . So here, let's just say, Solving quadratic equations by factoring. However, while the students are doing the practice problems, they can use the Hint feature for missed questions to view a step-by-step solution to the problem. This Kahoot!'er makes it easy for people learning or teaching . Quadratic functions & equations: FAQ. We. No ads, no subscriptions just 100% free, forever. Learn pre-algebraall of the basic arithmetic and geometry skills needed for algebra. Yes. https://www.khanacademy.org/math/algebra/quadratics/solving_graphing_quadratics/v/graphing-a-parabola-using-roots-and-vertex?utm_source=YT\u0026utm_medium=Desc\u0026utm_campaign=AlgebraIAlgebra I on Khan Academy: Algebra is the language through which we describe patterns. Khan Academy's Precalculus course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience! So x has to be equal to h. So one way to think about In this topic you will learn about the most useful math concept for creating video game graphics: geometric transformations, specifically translations, rotations, reflections, and dilations. The title is "Intro to parabola transformations". All that does is shift the vertex of a parabola to a point (h,k) and changes the speed at which the parabola curves by a factor of a ( if a is negative, reflect across x axis, if a=0 < a < 1, then the parabola will be wider than the parent function by a factor of a, if a = 1, the parabola will be the same shape as the parent function but translated.
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