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) = 0.56x²

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 downward
b the graph of h(x) is wider
c the graph of h(x) opens upward
d the graph of h(x) is narrower

Explanation:

The parent quadratic function is \( y = x^2 \), which has \( a = 1 \) (positive, so opens upward) and a vertical stretch factor of 1. For the function \( h(x)=0.5x^2 \), the coefficient \( a = 0.5 \) is positive, so the graph opens upward (matching option C). When \( |a| \) is between 0 and 1, the graph is wider than the parent function (since \( 0.5<1 \), the graph of \( h(x) \) is wider, matching option B). Option A is incorrect because \( a \) is positive, not negative. Option D is incorrect because a coefficient with absolute value less than 1 makes the graph wider, not narrower.

Answer:

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