Question

the graph of $y = x^2$ is shown on each grid in parts (a) and (b) below.
(a) use transformations to get the graph of $y = (-2x)^2$.

Explanation:

Step1: Simplify the transformed function

$y=(-2x)^2 = (2x)^2 = 4x^2$

Step2: Identify horizontal transformation

For $y=f(kx)$, $|k|>1$ shrinks $y=f(x)$ horizontally by $\frac{1}{|k|}$. Here $k=2$, so shrink $y=x^2$ horizontally by $\frac{1}{2}$.

Step3: Verify key points

Original $y=x^2$ points: $(1,1), (2,4)$. Transformed points: $(\frac{1}{2},1), (1,4)$.

Answer:

The graph of $y=(-2x)^2$ is a horizontal shrink of $y=x^2$ by a factor of $\frac{1}{2}$, passing through points like $(\frac{1}{2},1)$, $(1,4)$, $(-\frac{1}{2},1)$, $(-1,4)$, with vertex still at $(0,0)$.