Question

The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown. f(x) = 4(x2 + 12x) + 10 (twelve-halves) squared = 36 What is the function written in vertex form?

Answer 1

Answer:

$f(x)=4(x+6)^2-134$

Step-by-step explanation:

We are required to write the function$f(x) = 4x^2 + 48x + 10$ in vertex form.

First, bring the constant to the left-hand side.

$f(x) -10= 4x^2 + 48x$

Factorize the right hand side.

$f(x) -10= 4(x^2 + 12x)$

Take note of the factored term(4) and write it in the form below.

$f(x) -10+4\Box= 4(x^2 + 12x+\Box)$

$\Box = (\frac{\text{Coefficient of x}}{2} )^2\\\\\text{Coefficient of x}=12\\\\\Box = (\frac{12}{2} )^2 =6^2=36$

Substitute 36 for the boxes.

$f(x) -10+4\boxed{36}= 4(x^2 + 12x+\boxed{36})$

$f(x) -10+144= 4(x^2 + 12x+6^2)$

$f(x) +134= 4(x+6)^2\\f(x)=4(x+6)^2-134$

The function written in vertex form is $f(x)=4(x+6)^2-134$