Question

For the equation y=3x^2−6x−5, find the vertex showing all work.

Answer 1

vertex: (1, –8)

Explanation:

`a=3 \\b=-6\\c=-5`

rewrite equation in vertex form:
`y=a(x-h)^2+k`

1. factor out 3

`y=3x^(2) -6x-5\\y=3(x^(2)-2x)-5\\`

2. complete the square using
`((b)/(2) )^(2)`:

`((-2)/(2))^2=1`

3. add the answer from step 2 to inside the parenthesis to create a factorable trinomial. subtract the answer from step 2 from –5 and multiply it by a. remember: a = 3

`y=3(x^(2) -2x+1)-5-1(3)\\y=3(x-1)(x-1)-8\\y=3(x-1)^2-8`

4. find vertex

`x-1=0\\x=1`
`y=-8`

vertex =
`(1,-8)`