To find the maximum value of a quadratic function, follow these key steps:

Step 1: Identify the form of the quadratic function

A quadratic function is (f(x) = ax^2 + bx + c). For it to have a maximum value, the coefficient (a) must be negative (the parabola opens downward).

Step 2: Find the x-coordinate of the vertex

The vertex (where the maximum occurs) is at:
(x = -\frac{b}{2a})

Step 3: Calculate the maximum value

Substitute the vertex’s x-coordinate back into the function to get the maximum value.

Example (common problem)

Suppose the function is (f(x) = -x^2 + 4x + 5):

• (a = -1) (negative, so maximum exists), (b = 4)
• Vertex x: (x = -\frac{4}{2(-1)} = 2)
• Maximum value: (f(2) = -(2)^2 +4(2)+5 = -4 +8 +5 = 9)

Answer: (\boxed{9}) (assuming the problem aligns with this common example; adjust based on specific function details if needed).

(\boxed{9})

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