Question

For the following quadratic regression equation find the maximum y-value :

y= -0.582x^2 - 0.388x +52.147

Answer 1

To find the maximum y-value, we need to determine the vertex of the quadratic equation. The x-coordinate of the vertex can be found using the formula x = -b / 2a, where a = -0.582 and b = -0.388.

x = -(-0.388) / (2*-0.582)

x = 0.388 / -1.164

x = -0.3333

Now plug in this x-value into the quadratic equation to find the corresponding y-value:

y = -0.582(-0.3333)^2 - 0.388(-0.3333) + 52.147

y ≈ 53.069

Therefore, the maximum y-value for the quadratic regression equation is approximately 53.069.