Your friend is taking an algebra class at a different school where she is not allowed to use a graphing calculator. Explain to her how she can get a good sketch of the graph of the function $y = 2\left(x + 3\right)^{2} − 8$ without using a calculator and without having to make an $x → y$ table.

1. Be sure to explain how to locate the vertex, whether the parabola should open up or down, and how its shape is related to the shape of the graph of $y = x^{2}$.

   Answer (a):

   The graph has a vertex at $\left(−3, −8\right)$, opens up, and is vertically stretched.

2. Your friend also needs to know the x- and y-intercepts. Show her how to find them without having to draw an accurate graph or use a graphing calculator.