Which equation is y = 9x2 + 9x - 1 rewritten in vertex form?

1) y = 9 (x + one-half) squared minus thirteen-fourths

2) y = 9 (x + one-half) squared minus 1

3) y = 9 (x + one-half) squared + five-fourths

4) y = 9 (x + one-half) squared minus five-fourths

1. y = 9 (x+1/2) ^2 - 13/4

Step-by-step explanation:

y = 9x^2 + 9x - 1

first isolate the x terms

y = 9 (x^2 + x) - 1

then add 1/4 inside the brackets to make it a perfect square trinomial (half of the coefficient of the x term squared is how we get 1/4)

since we just added 1/4 we need to subtract what we just added to balance the equation. so 1/4 times 9 is 9/4 (the number we just added to the equation). then you subtract 9/4 outside of the brackets.

y = 9 (x^2 + x + 1/4) - 1 - 9/4

then simplify

y = 9 (x+1/2) ^2 - 13/4