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What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?
What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?
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What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?
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The minimum value occurs at x = -b/(2a) = -2/(2k). Setting f(-1) = -3 gives k = -2.
Questions & Step-by-step Solutions
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Q: What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?
Solution:
The minimum value occurs at x = -b/(2a) = -2/(2k). Setting f(-1) = -3 gives k = -2.
Steps: 6
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Step 1: Identify the function f(x) = kx^2 + 2x + 1.
Step 2: Recognize that this is a quadratic function, which has a minimum value when x = -b/(2a).
Step 3: In the function, a = k and b = 2. So, the x value for the minimum is x = -2/(2k).
Step 4: Substitute x = -2/(2k) into the function f(x) to find the minimum value.
Step 5: Set the minimum value equal to -3, since we want the minimum value to be -3.
Step 6: Solve the equation f(-2/(2k)) = -3 for k.
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