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a. Sketch the graph of $y=x^{2}$b. Sketch the graph of $y=3 x^{2}$c. Sketch the graph of $y=\frac{1}{3} x^{2}$d. Describe the graph of $y=a x^{2}$ in terms of the graph of $y=x^{2}$ when $a > 1$e. Describe the graph of $y=a x^{2}$ in terms of the graph of $y=x^{2}$ when $0 < a < 1$

See the graphd) We notice that the graph $y=a x^{2}$ is stretched horizontally by factor $a$e) We notice that the graph $y=a x^{2}$ is stretched horizontally by factor $a$

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 5

Polynomial Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

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all right. So for the first part of this exercise, we need to sketch the graph of Why equals X squared. And I've already loaded that just for convenience. And for the second part of the question, we need to sketch the graph of y equals three x squared. So if I plug in zero for X, I get zero. That's our first point. If I plug in one for X, I get three times one, which is going to be three. If I plug in negative one, I also get three. So that parable is going to look something like this, and there's no curvature down there. Even though there should be. It's just kind of hard to draw. Uh, And so, for the next part of the question, we have to sketch the graph of Y equals 1/3 x squared. So that's gonna look something like this again. We have zero point. And then if I plug in, let's say let's say I plug in three for X Squared Perec's So I get nine as X squared and 1/3 of nine ist three. So if I go over to three and I have to go up to three, and then the same thing applies for negative three. So this per Abalo looks something like this. Okay, So for the next part of the question, we have to describe the graph of why equals Yeah, why equals a X squared when a is greater than one? So when a is greater than one, the graph of y equals X squared is going to stretch The parabola of the basic graph of y equals X squared. It's going to make it longer in skinnier. And then when a is between zero and one, then it compresses the graph. It sort of squishes it and makes it fatter. So we have, ah, bigger paro Ebola or sort of wider problem for smaller values of a between zero and one. And we have a longer, skinnier problem for values of a greater than one

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