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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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Verified step by step guidance
1
Identify the parent function given, which is \(g(x) = x^2\). This is a basic parabola that opens upward and has a standard width.
Look at the given function \(f(x) = \frac{3}{2} x^2\). Notice that the coefficient in front of \(x^2\) is \(\frac{3}{2}\), which is greater than 1.
Recall that when the coefficient of \(x^2\) in a quadratic function \(a x^2\) is greater than 1, the parabola becomes narrower compared to the parent function \(x^2\). If the coefficient is between 0 and 1, the parabola becomes wider.
Determine the direction the parabola opens by looking at the sign of the coefficient \(a\). Since \(\frac{3}{2}\) is positive, the parabola opens upward.
Combine these observations: because \(\frac{3}{2} > 1\), the graph of \(f(x)\) is narrower than \(g(x)\), and since the coefficient is positive, it opens upward.