Question

How do you write the vertex form equation of the parabola `y= -2x^2 + 12x - 13`?

Answer 1

`y = -2(x - 3)^2 + 5`

Explanation:

`y = - 2x^2 + 12x - 13`
x-coordinate of vertex:
`x = -b/(2a) = -12/-4 = 3`
y-coordinate of vertex:
`y(3) = -2(9) + 12(3) - 13 = 18 - 13 = 5`
Vertex form:
`y = -2(x - 3)^2 + 5`

Check:
Develop the vertex form:
`y = -2(x^2 - 6x + 9) + 5 = -2x^2 + 12 x - 13.` OK