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

Step-by-step explanation:

An equation in the vertex form is written as

Where the point (h, k) is the vertex of the equation.

For an equation in the form the x coordinate of the vertex is defined as

In this case we have the equation .

Where

Then the x coordinate of the vertex is:

The y coordinate of the vertex is replacing the value of in the function

Then the vertex is:

Therefore The encuacion excrita in the form of vertice is:

To find the coefficient a we substitute a point that belongs to the function

The point (0, -1) belongs to the function. Thus.

Then the written function in the form of vertice is

The vertex form of a parabolic function has the general formula:

f(x) = a(x-h)^2 + k where (h,k) represent the vertex of the parabola.

Therefore, to write the given equation in vertex form, we will need to transform it to the above formula as follows:

y = 9x^2 + 9x - 1  

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

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

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

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

y = 9(x + 1/2)^2 - 13/4 > The equation in vertex form

Step-by-step explanation:

Hope this helps    : )

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