### Home > INT3 > Chapter 2 > Lesson 2.2.4 > Problem2-103

2-103.

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

1. ​​If this parabola is a function, what is its equation?

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 $a$.

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

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

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

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: INT3 2-103 HW eTool