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

Question

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

Eva Abramson · Accepted Answer

#y=2(x+1/2)^2-17/2# #"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"#

Nathan Axel · Answer

#2(x+1/2)^2-17/2#

The vertex form of a quadratic equation looks like this: #y=a(x-h)^2+k#

To get our equation into this form, we need to complete the square, but first I want to make the #x^2# term have a coefficient of #1# (you'll notice that the #x# inside the vertex form has this): #2x^2+2x-8=2(x^2+x-4)#

To complete the square, we can use the following formula: #x^2+px+q=(x+p/2)^2-(p/2)^2+q#

Applying this to #x^2+x-4#, we get: #x^2+x-4=(x+1/2)^2-(1/2)^2-4=(x+1/2)^2-17/4#

Now we put this back into our original expression: #2((x+1/2)^2-17/4)=2(x+1/2)^2-17/2#

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

Genesis Allen · Answer

undefined The vertex form of the given quadratic function $ y = 2x^2 + 2x - 8 $ is $ y = 2(x + 0.5)^2 - 8.5 $.