# How do you write the equation in vertex form #x=3y^2+5y-9#?

##### 1 Answer

Please see the explanation.

#### Explanation:

The vertex form of a parabola of this type is:

where, **x** and **y** correspond to any point, **h** and **k** correspond to the point that is the vertex, **a** is the leading coefficient of the

Given:

Let's expand the square in equation [1], multiply the terms by **a**, and write it directly above equation [2]:

Please observe that

If we set second term in equation [1a] equal to the second term in equation [2a] and we substitute 3 for **a**, then we can solve for the value of k:

Substitute 3 for a:

This tells us that the first three terms in equation [2a] can be replaced by

Substitute

Simplify:

Equation [2d] is the vertex form for a parabola that opens to the right or left.

You can read that the vertex is at the point