Answer: a = 5
b = -33
Explanation:
They want you to put the quadratic in vertex form. You need to complete the square to do this.
x² + 10x - 8 >Make space to complete square
x² + 10x - 8 >Take middle term 10, divide by 2 then square
that
Use +25 to fill in to complete the square but you
can't just add 25 to an equation, it changes it.
You need to counterbalance it by also
subtract 25. so 25-25= 0 you are not changing
x² + 10x +25 - 8 -25 >Combine the -8 and -25
x² + 10x +25 - 33 >Factor the first 3 terms x² + 10x +25
(x+5)(x+5) -33 >(x+5)(x+5) = (x+5)²
(x+5)² - 33 >this is the form they wanted.
a = 5
b = -33