Question

Complete the square to write the equation "y=3x^2+6x-24" in graphing form?

Answer 1

`y =3(x +1)^2 -27`

vertex is `(-1, -27)`

Explanation:

vetex form is:

`y = a(x-h)^2+k` and the vertex is `(h, k)`

to get vertex form we must complete the square:

`y=3x^2+6x-24`

isolate the x terms:

`y +24 =3x^2+6x`

factor out 3 so the coefficient of `x^2` is 1 which is required to complete the square:

`y +24 =3(x^2+2x)`

now complete the square

`ax^2 +bx +c`, a = 1, `c= (1/2b)^2`

`c=(1/2(2))^2 = 1^2 = 1`

`y +24 +3c=3(x^2+2x +c)` notice `3c` added to the left side, that is because we have to add the same value to both sides and the right side has 3 factored out.

replace the `c`

`y +24 +3(1)=3(x^2+2x +1)`

finish the square:

`y +27=3(x +1)^2`

`y =3(x +1)^2 -27`

so our vertex is `(-1, -27)`

remember the form is `y = a(x-h)^2+k` so the sign of the h term changes.