Question

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

`f(x)=3(x+3)^(2)-27`

Explanation:

In the last step is missing the number 3 which is the second term of the binomial squared expression.

Basically, the complete step is

`f(x)=3(x+3)^(2)-27`

As you can see, the three inside the parenthesis is the missing part in the last step.

Answer 2

3

Explanation:

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

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

Factor out a 3

= 3(x^2 +6x)

Take the coefficient of x, divide by 2 and then square

6/2 = 3 3^2 =9

Remember the 3 out side 3*9 =27 so we are really adding 27

3(x^2+6x+9) -3*9

The number inside the parentheses added to x is b/2 or 6/2

3(x+3)^2 -27