How do you find a quadratic function maximum value or minimum value when the function is...?

y = a(x - h)^2 + k

The critical value is k.

If a is positive, k is a minimum value.

If a is negative, k is a maximum value.

Minimum Value Of Quadratic Function

for y = ax^2 + bx +c then if a is positive, the function has a minimum. If a is negative, the function has a maximum. Differentiate the function. You get 2ax+b. The minimum or maximum is where the dervative is 0 because this is where the slope is zero. This is because if the slope is not zero, then moving to the left or the right along the curve would result in a higher or lower value, so the points where the slope is not zero can't be maximums or minimums. Solve for x when the derivative 2ax+b is 0. You get x=-b/2a. This is the x position where the minimum or maximum occurs. Plug x=-b/2a into the original equation and you get the value of y at the min or max, which is the minimum or maximum of the function.