Question

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

Answer 1

The equation y = 9x2 + 9x - 1 rewritten in vertex form is y = 9(x + 0.5)2 - 1.25, achieved by completing the square.

Step-by-step explanation:

The equation y = 9x2 + 9x - 1 can be rewritten in vertex form by completing the square. The vertex form of a quadratic equation is given by y = a(x - h)2 + k, where (h,k) is the vertex of the parabola. To rewrite the equation in vertex form, we complete the square on the x-terms.

Steps to rewrite the equation in vertex form:

1. Factor out the coefficient of the x2 term from the first two terms: y = 9(x2 + x) - 1.
2. To complete the square, divide the coefficient of the x term by 2, square it, and add it inside the parenthesis: (1/2 * 1)2 = 0.25. So, add and subtract 0.25 inside the parenthesis: y = 9[(x + 0.5)2 - 0.52] - 1.
3. Multiply out the -0.52 by 9 and combine it with the constant term outside: y = 9(x + 0.5)2 - 9(0.5)2 - 1.
4. Calculate 9(0.25) - 1 = 2.25 - 1 = 1.25: y = 9(x + 0.5)2 - 1.25.

So, the vertex form of the equation y = 9x2 + 9x - 1 is y = 9(x + 0.5)2 - 1.25.

Answer 2

Vertex for X

`-(9)/(2(9)) = -(2)/(18) = -(1)/(9)`

Vertex for Y

`y = 9x^(2) + 9x - 1 \\y = 9(-(1)/(9))^(2) + 9(-(1)/(9)) - 1 \\y = 9((1)/(81)) - 1 - 1 \\y = (1)/(9) - 1 - 1 \\y = -(8)/(9) - 1 \\y = -1(8)/(9)`

Vertex
(h, k) = (⁻¹/₉, -1⁸/₉)