Question

what is the first step when rewriting y = 3x2 9x – 18 in the form y = a(x – h)2 k? 3 must be factored from 3x2 9x x must be factored from 3x2 9x 9 must be factored from 9x – 18 3 must be factored from 3x2 – 18

Answer 1

Option A - 3 must be factored from
`3x^2+9x`

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
`(9)/(4)` (square the half of 9)

`y=3(x^2+3x+(9)/(4)-(9)/(4))-18`

Step 3- Solve

`y=3(x+(3)/(2))^2-(27)/(4)-18`

`y=3(x+(3)/(2))^2-(99)/(4)`

This is in the form
`y = a(x -h)^2+k`

where, a= 3 ,
`k=(-99)/(4)` and
`h=(-3)/(2)`

Therefore, Option A is correct.

3 must be factored from
`3x^2+9x`

Answer 2

Steps in rewriting :
y = 3 x² + 9 x - 18 = 3 ( x² + 3 x ) - 18 = 3 (( x² + 3 x + 9/4 ) - 9/4) - 18 =
= 3 ( x + 3/2 )² - 27/4 - 18 = 3 ( x + 3/2 )² - 99/4
Answer:
A ) 3 must be factored from 3 x² + 9 x.