Determine the maximum value of the quadratic function by completing the square. 𝑓(𝑥)=−𝑥^2−10𝑥−4

Answer 1

One of the best ways to complete this problem is to convert the function to vertex form which will give you the vertex of the parabola at ( -5, 21) thus resulting in a maximum value of f(x) = 21.

To step through the process... first note that the vertex form of a parabola is f(x) = a(x - h)² + k where ( h, k) is the resulting vertex.

With f(x) = -x² - 10x - 4, we must first complete the square to change to to vertex form.

f(x) = - (x² + 10x + 25 - 25) - 4

f(x) = - (x² + 10x + 25) + 25 - 4

f(x) = - (x + 5)² + 21 <-- The vertex is ( -5, 21).