Question

How do you write the quadratic in vertex form given `y=2x^2-12x+10`?

Answer 1

Standard form;`f(x) = ax^2 + bx + c`
Vertex form: `f(x) = a.[x + b/(2a)]^2 + f[-b/(2a)]`

`-b/(2a) = 12/4 = 3`

`f(3) = 2.(3)^2 - 12.(3) + 10 = 18 - 36 + 10 = -8`

Vertex form: `f(x) = 2.(x - 3)^2 - 8`

Check. Develop this vertex form:

`f(x) = 2.(x^2 - 6x + 9) - 8 = 2x^2 - 12x + 10`. Correct.