# What is the vertex form of #y=2x^2 +2x-8 #?

##### 2 Answers

#### Explanation:

The vertex form of a quadratic equation looks like this:

To get our equation into this form, we need to complete the square, but first I want to make the

To complete the square, we can use the following formula:

Applying this to

Now we put this back into our original expression:

And this is in vertex form, so it is our answer.

#### Explanation:

#"the equation of a parabola in "color(blue)"vertex form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#

#"where "(h,k)" are the coordinates of the vertex and a"#

#"is a multiplier"#

#"to express in this form use "color(blue)"completing the square"#

#• " ensure the coefficient of the "x^2" term is 1"#

#rArry=2(x^2+x-4)#

#• " add/subtract "(1/2"coefficient of x-term")^2" to"#

#x^2+x#

#y=2(x^2+2(1/2)x color(red)(+1/4)color(red)(-1/4)-4)#

#color(white)(y)=2(x+1/2)^ 2+2xx-17/4#

#rArry=2(x+1/2)^2-17/2larrcolor(red)"in vertex form"#