Question

Please help

The steps in writing f(x) = 18x + 3x2 in vertex form are shown, but a value is missing in the last step.



Write the function in standard form.

f(x) = 3x2 + 18x
Factor a out of the first two terms. f(x) = 3(x2 + 6x)
Form a perfect square trinomial.

f(x) = 3(x2 + 6x + 9) – 3(9)

Write the trinomial as a binomial squared. f(x) = 3(x + ______)2 – 27

What is the missing value in the last step?

Answer 1

3 is the missing value

Of there is any more help needed I can give you more tips and notes

Answer 2

The missing value in last step is 3

Explanation:

Given the function f(x)

`f(x)=18x+3x^2`

Here some steps are given to write the above function in vertex form.

Step 1: Factor a out of the first two terms

`f(x)=3(x^2+6x)`

Step 2: Form a perfect square trinomial.

`f(x) = 3(x^2 + 6x + 9) - 3(9)`

Write the trinomial as a binomial squared.

By the identity of binomial square

`a^2+2ab+b^2=(a+b)^2`

`x^2 + 6x + 9=x^2+2(x)(3)+3^2`

`\text{Put a=x and b=3 in the identity, we get}`

`x^2+2(x)(3)+3^2=(x+3)^2`

`x^2 + 6x + 9=(x+3)^2`

Hence, the f(x) can be written as

`f(x) = 3(x+3)^2 - 3(9)`

Therefore, the missing value in last step is 3