What is the maximum value of f(x) = -2x^2 + 10x - 12? (2022)

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Q: What is the maximum value of f(x) = -2x^2 + 10x - 12? (2022)

Solution: The maximum occurs at x = -b/(2a) = -10/(-4) = 2. f(2) = -2(2^2) + 10(2) - 12 = 6.

Steps: 13

Step 1: Identify the function f(x) = -2x^2 + 10x - 12.
Step 2: Recognize that this is a quadratic function in the form f(x) = ax^2 + bx + c, where a = -2, b = 10, and c = -12.
Step 3: To find the maximum value, use the formula for the x-coordinate of the vertex: x = -b/(2a).
Step 4: Substitute the values of a and b into the formula: x = -10 / (2 * -2).
Step 5: Calculate the denominator: 2 * -2 = -4.
Step 6: Now calculate x: x = -10 / -4 = 2.
Step 7: To find the maximum value of the function, substitute x = 2 back into the function f(x).
Step 8: Calculate f(2): f(2) = -2(2^2) + 10(2) - 12.
Step 9: Calculate 2^2 = 4, then -2(4) = -8.
Step 10: Calculate 10(2) = 20.
Step 11: Now combine the results: f(2) = -8 + 20 - 12.
Step 12: Calculate -8 + 20 = 12, then 12 - 12 = 0.
Step 13: Therefore, the maximum value of f(x) is 0.