Question

which of the following shows a vertical compression of the parent function f(x)=x²?
y = 3/5x²
y = -4x²

Explanation:

Step1: Recall vertical compression rule

For a parent function \( f(x) \), a vertical compression is given by \( g(x)=a f(x) \) where \( 0 < |a| < 1 \). The parent function here is \( f(x)=x^{2} \).

Step2: Analyze each function

• For \( y = \frac{3}{5}x^{2} \): Here \( a=\frac{3}{5} \), and \( 0<\frac{3}{5}< 1 \), so this is a vertical compression.
• For \( y=-4x^{2} \): Here \( |a| = 4>1 \), so this is a vertical stretch (and reflection over x - axis), not a compression.

Answer:

\( y=\frac{3}{5}x^{2} \) (the blue boxed function)