Complete a chart then sketch the graph of \( f(x)=x^{2} \). Complete a chart then sketch the graph of \( f(x)=4 x^{2} \). Compare the 2 sketches. What Transformation occurs as a result of the coefficient of 4 ? Vertical Stretch by 4 Units (More Narrow) Reflection Shift 4 Units Uper the \( x \)-axis 4 times Vertical Shrink by 4 Units (Wider)

To complete the charts for the functions \( f(x) = x^2 \) and \( f(x) = 4x^2 \), you can choose several values for \( x \), calculate \( f(x) \), and plot the points. For example, using values from -2 to 2 will give you: **For \( f(x) = x^2 \)**: - \( x = -2 \): \( f(-2) = 4 \) - \( x = -1 \): \( f(-1) = 1 \) - \( x = 0 \): \( f(0) = 0 \) - \( x = 1 \): \( f(1) = 1 \) - \( x = 2 \): \( f(2) = 4 \) **For \( f(x) = 4x^2 \)**: - \( x = -2 \): \( f(-2) = 16 \) - \( x = -1 \): \( f(-1) = 4 \) - \( x = 0 \): \( f(0) = 0 \) - \( x = 1 \): \( f(1) = 4 \) - \( x = 2 \): \( f(2) = 16 \) When you sketch these two graphs, you'll notice that while both are parabolas opening upwards, the graph of \( 4x^2 \) is narrower than that of \( x^2 \). The transformation caused by the coefficient of 4 leads to a vertical stretch, which makes the graph of \( f(x) = 4x^2 \) more narrow compared to that of \( f(x) = x^2 \). Essentially, the points get pulled away from the x-axis, resulting in a sharper rise as you move away from the vertex at the origin. This can be a fun way to visualize how changing coefficients affects the shape of quadratic functions!