Your friend is taking an algebra class at a different school where she is not allowed to use a graphing calculator.

1. Explain to her how she can get a good sketch of the graph of the function $y=2(x+3)^2−8$ without using a calculator and without having to make an $x→y$ table. 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 $y=x^2$.

   Hint (a):

   Where will the vertex be? Does the parabola open up or down? Is it 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.

   Hint (b):

   Substitute $0$ for $x$ and solve for $y$ to find the $y$-intercepts.
   Substitute $0$ for $y$ and solve for $x$ to find the $x$-intercepts.