Question

Write g(x) = 4x2 88x in vertex form. The function written in vertex form is g(x) = (x 11)2.

Answer 1

You can use the definition for the vertex form of a quadratic equation and then can can do conversion of that quadratic equation in that form.

The vertex form of the given equation is given by

$g(x) = 4(x+11)^2 - 484$

What is vertex form of  a quadratic equation?

If a quadratic equation is written in the form

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

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

This point is called the vertex of the parabola that quadratic equation represents.

How to convert the given equation to vertex form?

We first take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.

The given equation is $g(x) = 4x^2 + 88x$

Converting it in vertex form, we get:

$g(x) = 88x + 4x^2\\\\\\g(x) = 4x^2 + 88x\\g(x) = 4(x^2 + 22x)\\g(x) = 4(x^2 + 22x +121 - 121) \\g(x)=4(x+11)^2 - 484\text{\: (Note how the form} \: a^2 + b^2 + 2ab = (a+b)^2 \:\rm got\: made)$

Thus, we have h = -11 and k = -484

The plot of the given equation is attached below.

Thus,

The vertex form of the given equation is given by

$g(x) = 4(x+11)^2 - 484$

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