What is the vertex of the parabola represented by the equation y = 2x^2 - 8x + 5

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Question: What is the vertex of the parabola represented by the equation y = 2x^2 - 8x + 5?

Options:

Correct Answer: (2, -3)

Solution:

The vertex can be found using x = -b/(2a) = 4. Substituting x = 4 into the equation gives y = -3.

What is the vertex of the parabola represented by the equation y = 2x^2 - 8x + 5?

What is the vertex of the parabola represented by the equation y = 2x^2 - 8x + 5?

Correct Answer: (4, -3)

Step 1: Identify the coefficients from the equation y = 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).
Step 3: Substitute the values of a and b into the formula: x = -(-8)/(2*2).
Step 4: Simplify the calculation: x = 8/4 = 2.
Step 5: Now, substitute x = 2 back into the original equation to find the y-coordinate: y = 2(2^2) - 8(2) + 5.
Step 6: Calculate y: y = 2(4) - 16 + 5 = 8 - 16 + 5 = -3.
Step 7: The vertex of the parabola is (2, -3).

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