Question

What is the vertex form of 2x^2+6x-8?

Answer 1

Formula

`f(x)=a(x-p)^2+q` , V = (p,q)


`f(x)=2x^2+6x-8\\\\\ f(x)=ax^2+bx+c\\\\ a=2 \ , \ b=6 \ , \ c=-8 \\\\ p=(-b)/(2a)=(-6)/(\\ot2* 2)=-(3)/(2)\\\\q=(-\Delta)/(4a)=(-(b^2-4ac))/(4a)=(-[6^2-4*2*(-8)])/(4*2)=(-100)/(8)=-(25)/(2)`

`f(x)=2(x-(-(3)/(2))^2+(-(25)/(2))`

Answer

`f(x)=2(x+(3)/(2))^2-(25)/(2)\\\\ or\\\\ f(x)=2(x+1.5)^2-12.5`

V = (p,q) = (-1.5 ; -12.5)