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)

Answer 2

The vertex of a parabola is a point at which the parabola is minimum (when the parabola opens up) or maximum (when the parabola opens down) and the parabola turns (or) changes its direction.

The equation of vertex of parabola in perfect square trinomial form is $\rm g(x) = 4(x + 5)^2 - 100$

The vertex of the parabola is (-5, -100).

Given

Write g(x) = 40x + 4x2 in vertex form.

What is vertex form of parabola?

The vertex of a parabola is a point at which the parabola is minimum (when the parabola opens up) or maximum (when the parabola opens down) and the parabola turns (or) changes its direction.

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

$\rm f(x) = a(x-h)^2+ k$

The equation of vertex of parabola in perfect square trinomial form is;

$\rm g(x) = 4x^ + 40x\\\\ = 4[x^2+ 10x]\\\\ = 4((x + 5)^2 - 5^2)\\\\ = 4(x + 5)^2 - 100$

The vertex of the parabola is (-5, -100).

To know more about Vertex of Parabola click the link given below.

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