Question

Find the maximum/minimum value of the quadratic function x^2 – 10x = y + 40 by completing the square method.

A) Maximum value is 90.
B) Minimum value is -15.
C) Maximum value is 15.
D) Minimum value is -90.

Answer 1

To find the maximum/minimum value of the quadratic function x^2 – 10x = y + 40 using the completing the square method, we need to rewrite the equation in the form (x - h)^2 + k, where (h, k) represents the vertex of the quadratic function. The minimum value of the quadratic function is -65.

Step-by-step explanation:

To find the maximum/minimum value of the quadratic function x^2 – 10x = y + 40 using the completing the square method, we need to rewrite the equation in the form (x - h)^2 + k, where (h, k) represents the vertex of the quadratic function.

In this case, we have x^2 - 10x = y + 40. Moving the constant term to the other side, we get x^2 - 10x - y - 40 = 0. Completing the square, we add and subtract the square of half of the x coefficient, which is (-10/2)^2 = 25, giving us:

(x^2 - 10x + 25) - 25 - y - 40 = 0. Simplifying, we get (x - 5)^2 - y - 65 = 0. Rearranging the terms, we have:

(x - 5)^2 = y + 65. Comparing this with the standard form (x - h)^2 + k, we see that the vertex is located at (5, -65).

Therefore, the minimum value of the quadratic function is -65.