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