Question

Express the equation (y – 6) = (x + 4) in the form y = a(z - h)^2 + k, then identify a, h, and k.

a) y = (x + 4)^2 + 6; a = 1, h = -4, k = 6
b) y = (x - 4)^2 + 6; a = 1, h = 4, k = 6
c) y = (x + 4)^2 - 6; a = 1, h = -4, k = -6
d) y = (x - 4)^2 - 6; a = 1, h = 4, k = -6

Answer 1

To express the equation (y – 6) = (x + 4) in the form y = a(z - h)^2 + k, the equation must be rearranged. The correct form is y = (x - 4)^2 - 6, with a = 1, h = 4, and k = -6.

Step-by-step explanation:

To express the equation (y – 6) = (x + 4) in the form y = a(z - h)^2 + k, we need to rearrange it. Adding 6 to both sides, we get (y - 6) + 6 = (x + 4) + 6, which simplifies to y = x + 10. From this form, we can see that a = 0, h = -10, and k = 0.

Therefore, the correct option is d) y = (x - 4)^2 - 6, with a = 1, h = 4, and k = -6.