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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: \(f(x) = \frac{3}{2}x^2\) and \(g(x) = x^2\).
Recall that the graph of \(y = ax^2\) is a parabola that opens upward if \(a > 0\) and downward if \(a < 0\).
Since the coefficient of \(x^2\) in \(f(x)\) is \(\frac{3}{2}\), which is positive, the parabola opens upward.
Compare the coefficients to determine the width: the larger the absolute value of \(a\), the narrower the parabola; the smaller the absolute value, the wider it is.
Because \(\frac{3}{2} > 1\), the graph of \(f(x)\) is narrower than the graph of \(g(x)\).