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

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.