Answer:
vertex: (1, –8)
Step-by-step explanation:
[tex]a=3 \\b=-6\\c=-5[/tex]
rewrite equation in vertex form: [tex]y=a(x-h)^2+k[/tex]
1. factor out 3
[tex]y=3x^{2} -6x-5\\y=3(x^{2}-2x)-5\\[/tex]
2. complete the square using [tex](\frac{b}{2} )^{2}[/tex]:
[tex](\frac{-2}{2})^2=1[/tex]
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
[tex]y=3(x^{2} -2x+1)-5-1(3)\\y=3(x-1)(x-1)-8\\y=3(x-1)^2-8[/tex]
4. find vertex
[tex]x-1=0\\x=1[/tex] [tex]y=-8[/tex]
vertex = [tex](1,-8)[/tex]
