Question

F ( x ) = x 2 − 4 x − 12



What is the vertex?

Answer 1

vertex; (2, -16)

Explanation:

`f(x)=x^(2)-4x-12`

Complete the square of this quadratic equation. Completing the square is a process used to convert a quadratic equation in standard form, into vertex form. This process involved, grouping the linear and quadratic terms, then factor out the coefficient of the quadratic term. After doing so, one must add a term to the quadratic equation to make the grouped part of the quadratic equation a perfect square. Then one will balance the equation and simplify. The additive inverse of the constant term that is added two (x) is the x-coordinate of the vertex. The constant is the y-coordinate of the vertex.

`f(x)=x^(2) - 4x - 12\\\\=(x^(2)-4x)-12\\\\=(x^(2)-4x+4)-12-4\\\\=(x-2)^2 -16\\\\vertex;(2,-16)`