# What is the vertex form of # 7y = - 13x^2 -15x + 2 #?

##### 1 Answer

#### Explanation:

First, get the equation into its typical form by dividing both sides by

#y=-13/7x^2-15/7x+2/7#

Now, we want to get this into vertex form:

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

First, factor the

#y=-13/7(x^2+15/13x)+2/7#

Now, we want the term in the parentheses to be a perfect square. Perfect squares come in the pattern

Here, the middle term

This means that we want to add the missing term in the parentheses to make the group equal to

#y=-13/7overbrace((x^2+15/13x+?))^((x+15/26)^2)+2/7#

The missing term at the end of the perfect square trinomial is

Now we add

#y=color(blue)(-13/7)(x^2+15/13x+color(blue)(225/676))+2/7+color(blue)?#

Notice that we haven't actually added

#225/676xx-13/7=225/52xx-1/7=-225/364#

Since we have actually added

#y=-13/7(x+15/26)^2+2/7+225/364#

Note that

#color(red)(y=-13/7(x+15/26)^2+329/364#

This is in vertex form, where the parabola's vertex is at

We can check our work by graphing the parabola:

graph{7y = - 13x^2 -15x + 2 [-4.93, 4.934, -2.466, 2.466]}

Note that