What is the maximum value of the function f(x) = -2x^2 + 8x - 5? (2019)
Practice Questions
1 question
Q1
What is the maximum value of the function f(x) = -2x^2 + 8x - 5? (2019)
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9
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The vertex occurs at x = -b/(2a) = 2. f(2) = -2(2^2) + 8(2) - 5 = 9.
Questions & Step-by-step Solutions
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Q
Q: What is the maximum value of the function f(x) = -2x^2 + 8x - 5? (2019)
Solution: The vertex occurs at x = -b/(2a) = 2. f(2) = -2(2^2) + 8(2) - 5 = 9.
Steps: 10
Step 1: Identify the function we are working with, which is f(x) = -2x^2 + 8x - 5.
Step 2: Recognize that this is a quadratic function in the form of ax^2 + bx + c, where a = -2, b = 8, and c = -5.
Step 3: To find the maximum value, we need to find the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/(2a).
Step 4: Substitute the values of a and b into the formula: x = -8/(2 * -2).
Step 5: Calculate the value: x = -8 / -4 = 2.
Step 6: Now that we have x = 2, we need to find the corresponding y-value (f(2)).
Step 7: Substitute x = 2 into the function: f(2) = -2(2^2) + 8(2) - 5.
