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

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  $3x^2+9x$

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.