Question

What is the vertex form of `y = 2x^2 + 8x − 3`?

Answer 1

`y=2(x+2)^2-11`

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 obtain this form use "color(blue)"completing the square"`

`• " the coefficient of the "x^2" term must be 1"`

`rArry=2(x^2+4x)-3`

`• " add/subtract "(1/2"coefficient of x-term")^2" to"`
`x^2+4x`

`y=2(x^2+2(2)xcolor(red)(+4)color(red)(-4))-3`

`color(white)(y)=2(x+2)^2-8-3`

`rArry=2(x+2)^2-11larrcolor(red)"in vertex form"`