What is the function f (x) = 3 (x^2-8x) + 10 written in vertex form

y = 3 (x - 4) ² - 38

Step-by-step explanation:

We need to complete the square on

y = 3 (x² - 8x) + 10

A quadratic equation is in the form of y = ax² + bx + c. To complete the square, take half of the b term (here, the b term is - 8), then square it ...

-8/2 = - 4

(-4) ² = 16

Now add and subtract that from the equation ...

y = 3 (x² - 8x + 16 - 16) + 10

Now pull out the - 16 from the parenthesis, be careful though, there is a multiplier of 3 in front of the parenthesis, so it come out as a positive - 48

y = 3 (x² - 8x + 16) + 10 - 48

x² - 8x + 16 is a perfect square trinomial (we did this by completing the square), so it factors to (x - 4) ², and 10 - 48 = - 38, so our equation becomes ...

y = 3 (x - 4) ² - 38

This is now in vertex form, which is either the minimum or maximum.

Vertex form is

y = a (x - h) ² + k, where (h, k) is the vertex. If a > 0, then the vertex is a minimum, if a < 0, then the vertex is a maximum.

Our vertex is (4, - 38)