Question

Expressing the equation below in the vertex form will give a value of y = _____. y = x^2-11x-6

Answer 1

The vertex form of the quadratic equation y = x^2 - 11x - 6 is y = (x - 5.5)^2 - 36.25 by completing the square.

Step-by-step explanation:

To express the equation y = x^2-11x-6 in vertex form, we need to complete the square which involves the following steps:

1. First, we factor out the coefficient of the x² term if it is not 1. In this case, the coefficient is 1, so we can move to the next step.
2. Rewrite the equation grouping the x terms: y = (x^2 - 11x) - 6.
3. Find the number that completes the square: (11/2)² = 30.25.
4. Add and subtract this number inside the parenthesis: y = (x^2 - 11x + 30.25) - 30.25 - 6.
5. Rewrite the perfect square trinomial as a square of a binomial: y = (x - 5.5)² - 36.25.

The vertex form of the given quadratic equation is y = (x - 5.5)² - 36.25.