Question

What is the vertex form of `y= 5x^2 + 5x -12`?

Answer 1

`vertex = (-1/2, -13.25)`

Explanation:

`y = 5x^2 + 5x - 12`

take 5 as a common factor from the first two terms

`y = 5(x^2 + x) - 12`

completing square

`y = 5(x^2 + x + (1/2)^2) - 12 -5/4`

for completing square you take half the coefficient of x and square it
and we subtract 5/4 because from completing square we get 1/4 so 1/4 times 5 is 5/4 because it is positive inside it must be negative then

`y = 5(x+1/2)^2 - 13.25`

from the law `y = (x - h)^2 + k`

the vertex is = `(-1/2, -13.25)`