Complete a chart then sketch the graph of \( f(x)=x^{2} \) Complete a chart then sketch the graph of \( f(x)=\frac{1}{4} x^{2} \) Compare the 2 sketches. What Transformation occurs as a result of the coefficient of \( \frac{1}{4} \) ? Vertical Shift Horizontal Shift Vertical Stretch (More Narrow) Vertical Shrink (Wider)

When you compare the graphs of \( f(x) = x^{2} \) and \( f(x) = \frac{1}{4} x^{2} \), you'll notice that the latter graph is wider than the former. To illustrate this, you can create a table of values for both functions. For example, when \( x = -2, -1, 0, 1, 2 \), the function \( f(x) = x^2 \) yields \( 4, 1, 0, 1, 4 \), while \( f(x) = \frac{1}{4} x^2 \) yields \( 1, \frac{1}{4}, 0, \frac{1}{4}, 1 \). The transformation caused by the coefficient \( \frac{1}{4} \) is a vertical shrink, stretching the graph horizontally. As you sketch the graphs, root for your favorite points! You'll find that while \( f(x) = x^{2} \) hugs the y-axis tightly, \( f(x) = \frac{1}{4} x^{2} \ sprawls out comfortably, showcasing that gentler curve. Think of it like a sleepy cat spread wide across the couch rather than a cat sitting upright! So, remember: the smaller the coefficient in front of \( x^{2} \), the wider the graph stretches. It’s all about lounging out and enjoying the extra space!