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.
Factor a out of the first two terms. f(x)=3(x2+6x)

Form a perfect square trinomial. (six-halves) squared

f(x)=3(x2+6x+9)−3(9)

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

Answer 1

3

Explanation:

f(x)=3(x+3)2−27

the missing value is 3

Answer 2

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

Explanation:

we have

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

Write the function in standard form

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

Factor 3 out of the first two terms

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

Form a perfect square trinomial. (six-halves) squared

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

`f(x)=3(x^(2)+6x+9)-27`

Write the trinomial as a binomial squared

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

therefore

The vertex is the point (-3,-27)