# What is the vertex form of #y=(5x-5)(x+20)#?

##### 1 Answer

vertex form:

#### Explanation:

**1. Expand.**

Rewrite the equation in standard form.

#y=(5x-5)(x+20)#

#y=5x^2+100x-5x-100#

#y=5x^2+95x-100#

**2. Factor 5 from the first two terms.**

#y=5(x^2+19x)-100#

**3. Turn the bracketed terms into a perfect square trinomial.**

When a perfect square trinomial is in the form

#y=5(x^2+19x+(19/2)^2)-100#

#y=5(x^2+19x+361/4)-100#

**4. Subtract 361/4 from the bracketed terms.**

You can't just add

#y=5(x^2+19x+361/4# #color(red)(-361/4))-100#

**5. Multiply -361/4 by 5.**

You then need to remove the

#y=color(blue)5(x^2+19x+361/4)-100[color(red)((-361/4))*color(blue)((5))]#

**6. Simplify.**

#y=5(x^2+19x+361/4)-100-1805/4#

#y=5(x^2+19x+361/4)-2205/4#

**7. Factor the perfect square trinomial.**

The last step is to factor the perfect square trinomial. This will tell you the coordinates of the vertex.

#color(green)(y=5(x+19/2)^2-2205/4)#