What is the vertex of the quadratic function f(x) = 2x^2 - 8x + 6?

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Question: What is the vertex of the quadratic function f(x) = 2x^2 - 8x + 6?

Options:

Correct Answer: (2, -2)

Solution:

The vertex can be found using the formula x = -b/(2a), which gives x = 2. Substituting x back into the function gives the y-coordinate.

What is the vertex of the quadratic function f(x) = 2x^2 - 8x + 6?

What is the vertex of the quadratic function f(x) = 2x^2 - 8x + 6?

Step 1: Identify the coefficients from the quadratic function f(x) = 2x^2 - 8x + 6. Here, a = 2, b = -8, and c = 6.
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: Calculate the value: x = 8/4 = 2. This is the x-coordinate of the vertex.
Step 4: To find the y-coordinate of the vertex, substitute x = 2 back into the function: f(2) = 2(2^2) - 8(2) + 6.
Step 5: Calculate f(2): f(2) = 2(4) - 16 + 6 = 8 - 16 + 6 = -2. This is the y-coordinate of the vertex.
Step 6: Combine the x and y coordinates to find the vertex: The vertex is (2, -2).

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