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) (ten-halves) squared = 25 g(x) = 4(x2 10x 25) – 4(25) g(x) = (x )2 –.

Answer 1

The vertex form of the function g(x)=40x-4x² is g(x) = 4(x + 5)² - 100, where the vertex lies at (-5, -100).

What is the Equation of a parabola?

The  general equation of a parabola is given as,

y = a(x-h)² + k

where,

(h, k) are the coordinates of the vertex of the parabola in form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

As we want to write a function g(x) = 40x + 4x² in vertex form, and we know that the vertex form of a parabola, with vertex at (h,k) is written as,

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

Also, the algebraic identity  $(x + a)^2$ is written as,

$(x + a)^2 = x^2 + 2ax + a^2$,

Therefore, $x^2 + 2ax$ can be written as

$x^2 + 2ax = (x + a)^2 - a^2$

Further, we try to write the g(x) in the vertex form it can be written as,

$\begin{aligned}g(x) &= 4x^2 + 40x\\\\ &= 4[x^2 + 10x]\\\\ &= 4[(x + 5)^2 - 5^2]\\\\ &= 4(x + 5)^2 - 100\\\end{aligned}$

Hence, the vertex form of the function g(x)=40x-4x² is g(x) = 4(x + 5)² - 100, where the vertex lies at (-5, -100).

Learn more about Parabola:

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