Answer:
Option A - 3 must be factored from [tex]3x^2+9x[/tex]
Step-by-step explanation:
Given : Function [tex]y=3x^2+9x-18[/tex]
To find : What is the first step when rewriting [tex]y=3x^2+9x-18[/tex] in the form [tex]y = a(x -h)^2+k[/tex].
Solution :
To convert into the form [tex]y = a(x -h)^2+k[/tex] we follow the steps as:
Function [tex]y=3x^2+9x-18[/tex]
Step 1- 3 must be factored from [tex]3x^2+9x[/tex]
[tex]y=3(x^2+3x)-18[/tex]
Step 2 - Completing the square by adding and subtracting [tex]\frac{9}{4}[/tex] (square the half of 9)
[tex]y=3(x^2+3x+\frac{9}{4}-\frac{9}{4})-18[/tex]
Step 3- Solve
[tex]y=3(x+\frac{3}{2})^2-\frac{27}{4}-18[/tex]
[tex]y=3(x+\frac{3}{2})^2-\frac{99}{4}[/tex]
This is in the form [tex]y = a(x -h)^2+k[/tex]
where, a= 3 , [tex]k=\frac{-99}{4}[/tex] and [tex]h=\frac{-3}{2}[/tex]
Therefore, Option A is correct.
3 must be factored from [tex]3x^2+9x[/tex]
