Question

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

Answer 1

Answer:

vertex: (1, –8)

Step-by-step 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 $(\frac{b}{2} )^{2}$:

$(\frac{-2}{2})^2=1$

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 = $(1,-8)$