Question

1. the graph of f(x) = ax² opens upward and is narrower than the graph of g(x) = x². which of the following could be the value of a? a -0.5 b 6 c 0.25 d -2

Explanation:

Step1: Recall parabola direction rule

For \( f(x) = ax^2 \), if \( a>0 \), the parabola opens upward; if \( a<0 \), it opens downward. So \( a \) must be positive. Eliminate options A (\(-0.5\)) and D (\(-2\)) as they are negative.

Step2: Recall parabola width rule

The width of \( f(x) = ax^2 \) compared to \( g(x)=x^2 \): if \( |a| > 1 \), \( f(x) \) is narrower; if \( |a| < 1 \), \( f(x) \) is wider. We need \( |a| > 1 \) (narrower) and \( a>0 \) (opens upward).

• Option B: \( a = 6 \), \( |6| = 6>1 \) and \( 6>0 \).
• Option C: \( a = 0.25 \), \( |0.25| = 0.25<1 \), so it's wider, not narrower.

Answer:

B. 6