Answer:
y=8(x+1)²-2
Step-by-step explanation:
Completing the square is a method of factorising. x²+bx+c=0 becomes x²+bx+([tex]\frac{1}{2}[/tex]b)²-([tex]\frac{1}{2}[/tex]b)²+c=0. This then gets converted to make an equation of (x+[tex]\frac{1}{2}[/tex]b)²+(-([tex]\frac{1}{2}[/tex]b)²+c)=0.
Vertex form is y=a(x-h)²+k.
8x²+16x+6=0 must first be divided by 8 to 8(x²+2x+[tex]\frac{6}{8}[/tex])=0 (as there cannot be a coefficient for x²).
This will become 8(x²+2x+[tex]\frac{2}{2}[/tex]²-[tex]\frac{2}{2}[/tex]²+[tex]\frac{3}{4}[/tex])=0.
From there, using the method above, we can convert it to 8[(x+1)²-1+[tex]\frac{3}{4}[/tex]]=0.
Solving this gets 8[(x+1)²-[tex]\frac{1}{4}[/tex]]=0.
With 8 as a, 1 as -h, and 8×-[tex]\frac{1}{4}[/tex] (-2) as k, we can input this into vertex format to get the result of y=8(x+1)²-2.
**This equation involves completing the square and vertex form, which you may wish to revise. I'm always happy to help!
