Question

how does the value of a in the function affect its graph when compared to the graph of the quadratic parent function?
h(x) = -0.13x²

in what ways is the graph of h(x) different from the graph of the parent function? select all that apply
□ a. the graph of h(x) is wider
□ b. the graph of h(x) opens upward
□ c. the graph of h(x) opens downward
□ d. the graph of h(x) is narrower

Explanation:

Step1: Recall quadratic function properties

The parent quadratic function is \( y = x^2 \), with \( a = 1 \), opening upward, and the "width" is determined by \( |a| \). For \( h(x)= - 0.13x^2 \), \( a=- 0.13 \).

Step2: Analyze the sign of \( a \)

The sign of \( a \) determines the direction the parabola opens. If \( a>0 \), opens upward; if \( a < 0 \), opens downward. Here \( a=-0.13<0 \), so it opens downward (so option C is correct, B is incorrect).

Step3: Analyze \( |a| \) for width

The magnitude \( |a| \) affects the width: if \( |a|>1 \), the graph is narrower than \( y = x^2 \); if \( 0<|a|<1 \), the graph is wider. Here \( | - 0.13|=0.13 \), and \( 0 < 0.13<1 \), so the graph is wider (so option A is correct, D is incorrect).

Answer:

A. The graph of \( h(x) \) is wider
C. The graph of \( h(x) \) opens downward