Question

Rewrite y=x^2-10x-6 in vertex form.

Answer 1

To rewrite the quadratic equation y=x^2-10x-6 in vertex form, we can complete the square. The vertex form of a quadratic equation is y=a(x-h)^2+k, where (h,k) represents the vertex of the parabola. To complete the square, group the x-terms together and rewrite x^2-10x as (x^2-10x+25)-25 by adding and subtracting half the coefficient of the x-term squared.

Step-by-step explanation:

To rewrite the quadratic equation y=x^2-10x-6 in vertex form, we can complete the square. The vertex form of a quadratic equation is y=a(x-h)^2+k, where (h,k) represents the vertex of the parabola.

To complete the square, we need to group the x-terms together:

y=(x^2-10x)-6

We can rewrite x^2-10x as (x^2-10x+25)-25 by adding and subtracting the square of half the coefficient of the x-term (in this case, 25).

So, the equation becomes: y=(x^2-10x+25)-25-6

Simplifying further, we get: y=(x-5)^2-31

Answer 2

The vertex form is y= (x - 5)^2 - 31