Question

how does the value of a in the function affect its graph when compared to the graph of the quadratic parent function?
$h(x) = -0.87x^2$
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 $h(x)$ opens upward
b. the graph of $h(x)$ is wider
c. the graph of $h(x)$ opens downward
d. the graph of $h(x)$ is narrower.

Explanation:

The parent quadratic function is \( y = x^2 \), which opens upward. For a quadratic function \( y = ax^2 \), if \( a>0 \), the parabola opens upward; if \( a < 0 \), it opens downward. Here, \( a=- 0.87<0 \), so the graph of \( h(x)=-0.87x^{2} \) opens downward (so option C is correct, A is incorrect). Also, the absolute value of \( a \) determines the width: if \( |a|>1 \), the graph is narrower; if \( 0 < |a|<1 \), the graph is wider. Since \( | - 0.87|=0.87<1 \), the graph of \( h(x) \) is wider (so option B is correct, D is incorrect).

Answer:

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