Question

How do convert =x^2+2x-3 to vertex form?

Answer 1

`y=(x+1)^2-4`

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 we can "color(blue)"complete the square"`

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

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

`rArry=x^2+2(1)xcolor(red)(+1)color(red)(-1)-3`

`color(white)(rArry)=(x+1)^2-4larrcolor(red)"in vertex form"`
graph{x^2+2x-3 [-10, 10, -5, 5]}

Answer 2

Convert the standard form, `y=ax^2+bx+c` to the vertex form `y =a(x-h)^2+k` using the equations:

`a=a`

`h=-b/(2a)`

`k=ah^2+bh+c`

Explanation:

Given: `y = x^2+ 2x-3`

The vertex form is:

`y = a(x-h)^2+k" [1]"`

Substitute `a = 1`:

`y = (x-h)^2+k" [1.1]"`

Compute `h = -b/(2a)`

`h = -1`

`y = (x--1)^2+k" [1.3]"`

Compute `k = (-1)^2+2(-1)-3`

`k = -4`

`y = (x--1)^2+ (-4) larr` this is the vertex form