Question

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)

Answer 1

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)