Question

How do you rewrite `y=-3x^2-12x-2` rewritten in vertex form?

Answer 1

`y = -3(x-2)^2 + 10`

Explanation:

Vertex form of quadratic equation `ax^2 + bx + c` is
`y = a(x - x_s)^2 + y_s`

`x_s = -b / (2a)`

`y_s = -(b^2/4a) + c`

Given equation is
`y = -3x^2 -12x -2`
`a = -3, b = -12, c = -2`

`x_s =( -12) / (2*(-3)) = 2`
`y_s = -b^2/(4a) + c =-( -12^2) / (4 * -3) + (-2)= 10`

`y = -3 * ( x - 2)^2 + 10`