Question

How do you write `f(x)=-2(x-5)^2+3` in standard form? In which form is it easier to determine maximum value of the graph?

Answer 1

`f(x) = -2x^2 + 20x - 47`

Explanation:

First step is to square the term in parenthesis using cross multiplication:

`f(x) = -2(x - 5)(x - 5) + 3`

`f(x) = -2(x^2 - 5x - 5x + 25) + 3`

`f(x) = -2(x^2 - 10x + 25) + 3`

`f(x) = -2x^2 + 20x - 50 + 3`

`f(x) = -2x^2 + 20x - 47`