Question

Write x2 - 12x + 8 in vertex form.

Answer 1

Answer:

The answer to this is: y = (x - 6)² - 28

Step-by-step explanation:

The first step is to make sure the coefficient in front of x² is 1. If it isn't, just divide the whole equation by the coefficient. In this case, you don't need to do any division because you just have x²

Group the first two terms involving x² and x:

(x² - 12x) + 8

Now complete the square as follows:

a. Take the coefficient in front of x --> -12

b. Halve it --> -6

c. Square it --> (-6)² = 36

d. Add this and subtract it

(x² - 12x + 36 - 36) + 8

Take the negative number outside the parentheses:

(x² - 12x + 36) - 36 + 8

(x² - 12x + 36) - 28

The part in parentheses is a perfect square so rewrite it as such. If you need help refer back to step b.

(x - 6)(x - 6) - 28

(x - 6)² - 28

P.S. Vertex form is:

(x - h)² + k

In that form, the vertex is (h, k). In your case, the vertex of the parabola would be (6, -28).

Answer:

y = (x - 6)² - 28