Solve the following quadratic inequalities by graphing the corresponding function Looking at these questions and I am not confident in my abilities to solve them.

Solve the following quadratic inequalities by graphing the corresponding function. Note: a) and b) are separate questions.
  $$ a) y \le -2x^2+16x-24\\
b) y > \frac 13 (x-1)^2-3
$$

Help would be appreciated!

You don't solve these inequalities for points on a curve; these statements describe regions of the plane (so you would "color in" a portion of the graph accordingly).
For the first one, we want all the points which are below or on the parabola described by the quadratic polynomial. Since it is a "downward-facing" parabola (the quadratic coefficient is negative), you would select "everything inside" the parabola and the parabola itself.
In the second one, you would only have the points above, but not on, the parabola (since this is a "proper inequality" -- no equation here).  The parabola "faces upward" in this problem (the quadratic coefficient is positive), so again you would "color in" all the points within the parabola, but not the parabola itself.
