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) = 7x²

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

Explanation:

The quadratic parent function is \( y = x^2 \), where \( a = 1 \), and it opens upward. For the function \( g(x)=7x^2 \), the coefficient \( a = 7 \). When \( |a|>1 \) in a quadratic function \( y = ax^2 \), the graph is narrower than the parent function \( y = x^2 \). Also, since \( a = 7>0 \), the graph opens upward, just like the parent function. So we analyze each option:

• Option A: Since \( |7|>1 \), the graph of \( g(x) \) is narrower than the parent function's graph. This is correct.
• Option B: The coefficient \( 7 \) is positive, so the graph opens upward. This is correct (and the parent function also opens upward, but this is still a property of \( g(x) \)'s graph).
• Option C: A wider graph would occur when \( |a|<1 \), but \( |7|>1 \), so this is incorrect.
• Option D: The coefficient is positive, so the graph does not open downward. This is incorrect.

Answer:

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