Question

exploring the graph of $y = ax^2$
as $|a|$ increases, the parabola becomes
wider.
narrower.
flat.
$a = 1$

Explanation:

Step1: Recall parabola transformation

For the quadratic function \( y = ax^2 \), the coefficient \( a \) affects the vertical stretch/compression of the parabola \( y = x^2 \).

Step2: Analyze \( |a| \) effect

• If \( |a| > 1 \), the graph is a vertical stretch (narrower) of \( y = x^2 \).
• If \( 0 < |a| < 1 \), the graph is a vertical compression (wider) of \( y = x^2 \).

As \( |a| \) increases, the vertical stretch increases, making the parabola narrower.

Answer:

narrower