# How do you write the equation of the parabola in vertex form given vertex (3,3) and focus: (-2,3)?

##### 2 Answers

The vertex form for the equation of a parabola whose focus is shifted horizontally a signed distance,

where

#### Explanation:

Substitute the vertex

Compute the signed distance from the vertex to the focus:

Substitute

Simplify the denominator:

#### Explanation:

First, let's figure out which way we need to draw the parabola.

The vertex is (3,3) and the focus is (-2,3).

These points have the same y-value, so they form a horizontal line. This means that the parabola will be horizontal.

It must be of the form

#x = a(y-k)^2+h# Additionally, the focus is to the LEFT of the vertex, so the parabola will point to the LEFT (meaning

#a# is negative).

Let's call the distance between the focus and the vertex

We know that the value of

#a# is equal to#+-1/(4c)# .In this case,

#c# is 5, since the vertex and focus are#5# units apart.

#a = +-1/(4(5)) = +- 1/20 = -1/20# since we already know#a# is negative.

This gives us everything we need to write our parabola's equation! The vertex

#x = a(y-k)^2 + h#

#x = -1/20(y-3)^2+3#

*Final Answer*