Write g (x) = 40x + 4x2 in vertex form. Write the function in standard form. Factor a out of the first two terms. Form a perfect square trinomial. Write the trinomial as a binomial squared. g (x) = 4x2 + 40x g (x) = 4 (x2 + 10x) = 25 g (x) = 4 (x2 + 10x + 25) - 4 (25)

We want to write g (x) = 40x + 4x² in vertext form.

Note that

The vertex form of a parabola, with vertex at (h, k) is

f (x) = a (x-h) ² + k

Also

(x + a) ² = x² + 2ax + a², so that

x² + 2ax = (x + a) ² - a²

Therefore

g (x) = 4x² + 40x

= 4[x² + 10x]

= 4[ (x + 5) ² - 5²]

= 4 (x + 5) ² - 100

Answer:

g (x) = 4 (x + 5) ² - 100.

g (x) is in vertex form, and the vertex is at (-5, - 100)