Mathematics: 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?

wwhywuikStep-by-step explanation:...

The first steps in writing f(x) = 4x2 + 48x + - id4248107089883, samanthashade8352

bestsonever698

30.01.2022

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

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