Your friend goes to a different school and she is not allowed to use a graphing calculator in her math class.

1. Explain to her how she can get a good sketch of the graph of the function $f(x) = -2(x - 3)^2 + 2$ without using a calculator and without making an $x$ → $y$ table. Be sure to explain how to locate the vertex, whether the parabola opens up or down, and how its shape is related to the shape of the graph of $f(x) = x^2$.

   Hint (a):

   There is a squared term, so this is a parabola.
   The stretch factor is $-2$. How does this affect the graph?
   Where is the vertex?

2. Your friend also needs to know the $x$- and $y$-intercepts. Help her determine them without drawing an accurate graph or using a graphing calculator.

   Hint (b):

   You can find the $x$- and $y$- intercepts by solving for $x$ when $y = 0$ and by solving for $y$ when $x = 0$.