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)