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Find the maximum value of the function f(x) = -x^2 + 6x - 8.
Find the maximum value of the function f(x) = -x^2 + 6x - 8.
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Practice Questions
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Q1
Find the maximum value of the function f(x) = -x^2 + 6x - 8.
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The vertex occurs at x = 3. f(3) = -3^2 + 6(3) - 8 = 6.
Questions & Step-by-step Solutions
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Q
Q: Find the maximum value of the function f(x) = -x^2 + 6x - 8.
Solution:
The vertex occurs at x = 3. f(3) = -3^2 + 6(3) - 8 = 6.
Steps: 7
Show Steps
Step 1: Identify the function you need to analyze, which is f(x) = -x^2 + 6x - 8.
Step 2: Recognize that this is a quadratic function in the form of f(x) = ax^2 + bx + c, where a = -1, b = 6, and c = -8.
Step 3: Find the x-coordinate of the vertex using the formula x = -b/(2a). Here, b = 6 and a = -1.
Step 4: Calculate x = -6/(2 * -1) = -6/-2 = 3.
Step 5: Now, substitute x = 3 back into the function to find the maximum value: f(3) = -3^2 + 6(3) - 8.
Step 6: Calculate f(3): f(3) = -9 + 18 - 8 = 1.
Step 7: The maximum value of the function is 1.
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