(b) Use transformations to get the graph of \( y=2 x^{2} \)

To understand the graph of \( y = 2x^2 \), start with the basic parabola, \( y = x^2 \), which opens upwards with its vertex at the origin (0, 0). The transformation here is multiplying the function by 2. This vertical stretch makes the parabola narrower, meaning it grows faster away from the x-axis, still maintaining its U-shape. Instead of rising one unit for each unit you move away from the vertex, it now rises two units! A fun fact: If you really want to visualize this, think of the parabola as a puppet on a string. When you pull the string tighter (by multiplying by 2), the puppet (the graph) moves up more sharply, creating that narrower effect! Always remember to plot a few points for a clearer view of how it transforms.