What is the vertex of the quadratic function f(x) = 2x^2 - 8x + 5? (2021)

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Question: What is the vertex of the quadratic function f(x) = 2x^2 - 8x + 5? (2021)

Options:

Correct Answer: (2, -3)

Exam Year: 2021

Solution:

The vertex can be found using x = -b/(2a). Here, x = 8/(2*2) = 2. Substituting x = 2 into f(x) gives f(2) = -3, so the vertex is (2, -3).

What is the vertex of the quadratic function f(x) = 2x^2 - 8x + 5? (2021)

What is the vertex of the quadratic function f(x) = 2x^2 - 8x + 5? (2021)

Step 1: Identify the coefficients a, b, and c from the quadratic function f(x) = 2x^2 - 8x + 5. Here, a = 2, b = -8, and c = 5.
Step 2: Use the formula for the x-coordinate of the vertex, which is x = -b/(2a). Substitute b and a into the formula: x = -(-8)/(2*2).
Step 3: Simplify the expression: x = 8/(4) = 2. This gives us the x-coordinate of the vertex.
Step 4: Now, substitute x = 2 back into the original function to find the y-coordinate: f(2) = 2(2^2) - 8(2) + 5.
Step 5: Calculate f(2): f(2) = 2(4) - 16 + 5 = 8 - 16 + 5 = -3.
Step 6: Combine the x and y coordinates to find the vertex: The vertex is (2, -3).

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