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Multiple Choice
State whether the graph of will be narrower or wider than & if it opens up or down.
A
Narrower; Down
B
Narrower; Up
C
Wider; Down
D
Wider; Up
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1
Identify the given functions: \( g(x) = x^2 \) and \( f(x) = -\frac{3}{7}x^2 \). Both are quadratic functions in the form \( ax^2 \).
Recall that the coefficient \( a \) in \( ax^2 \) affects the width and direction of the parabola. If \( |a| > 1 \), the graph is narrower than \( y = x^2 \); if \( |a| < 1 \), it is wider.
Compare the absolute value of the coefficient in \( f(x) \), which is \( \left| -\frac{3}{7} \right| = \frac{3}{7} \), to 1. Since \( \frac{3}{7} < 1 \), the graph of \( f(x) \) is wider than \( g(x) \).
Determine the direction the parabola opens by looking at the sign of \( a \). Since \( a = -\frac{3}{7} \) is negative, the parabola opens downward.
Summarize: The graph of \( f(x) = -\frac{3}{7}x^2 \) is wider than \( g(x) = x^2 \) and opens down.