A parabola has vertex $(3, 5)$ and contains the point $(0, 0)$.

1. If this parabola is a function, find its equation.

   Hint (a):

   Recall the standard form for the equation of a parabola: $y=a(x−h)^2+k$
   Substitute the appropriate values for the vertex $(h,k)$, and $x$ and $y(0,0)$, then solve for $a$.

   More Help (a):

   Refer to problem 2-127 in Lesson 2.2.3 if you need more help.

   Answer (a):

   $y=-\frac{5}{9}\left(x-3\right)^2+5$

2. Suppose this parabola is not a function, but is a “sleeping” parabola. Find its equation.

   Hint (b):

   Use the equation $x=a(y−k)^2+h$ where the vertex is at $(h,k)$.

   Use the eTool below to graph the equations.
   Click the link at right for the full version of the eTool: CCA2 2-146 HW eTool