Question

how does the value of a in the function affect its graph when compared to the graph of the quadratic parent function?
g(x)=5x²

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

Explanation:

The parent quadratic function is \( y = x^2 \). For a quadratic function \( y = ax^2 \):

• If \( |a|>1 \), the graph is narrower than the parent function. Here, \( a = 5 \), and \( |5|>1 \), so the graph of \( g(x)=5x^2 \) is narrower than \( y = x^2 \).
• If \( a>0 \), the parabola opens upward. Since \( 5>0 \), the graph of \( g(x) \) opens upward.
• Option A is incorrect because \( |a|>1 \) makes it narrower, not wider. Option D is incorrect because \( a>0 \) means it opens upward, not downward.

Answer:

B. The graph of \( g(x) \) is narrower, C. The graph of \( g(x) \) opens upward