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) = -0.26x²

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

Explanation:

Step1: Recall parent function properties

The quadratic parent function is \( y = x^2 \), which opens upward (since the coefficient of \( x^2 \) is positive, \( a = 1>0 \)) and has a "width" related to \( |a| \). For \( |a|>1 \), the graph is narrower; for \( 0<|a|<1 \), the graph is wider.

Step2: Analyze \( h(x)= - 0.26x^2 \)

• Sign of \( a \): The coefficient \( a=-0.26 \), which is negative. So the parabola opens downward (eliminating option A, confirming D).
• Magnitude of \( |a| \): \( | - 0.26|=0.26 \), and \( 0 < 0.26<1 \). So the graph is wider than the parent function (since \( |a| < 1 \)), eliminating B, confirming C.

Answer:

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