What is the vertex of the quadratic function y = 2x^2 - 8x + 5?

What is the vertex of the quadratic function y = 2x^2 - 8x + 5?

Step 1: Identify the coefficients a and b from the quadratic function y = 2x^2 - 8x + 5. Here, a = 2 and b = -8.
Step 2: Use the formula to find the x-coordinate of the vertex: x = -b / (2a).
Step 3: Substitute the values of a and b into the formula: x = -(-8) / (2 * 2).
Step 4: Simplify the expression: x = 8 / 4, which equals 2.
Step 5: Now, find the y-coordinate of the vertex by plugging x = 2 back into the original equation: y = 2(2)^2 - 8(2) + 5.
Step 6: Calculate y: y = 2(4) - 16 + 5, which simplifies to y = 8 - 16 + 5.
Step 7: Further simplify: y = -8 + 5, which equals -3.
Step 8: Combine the x and y coordinates to find the vertex: The vertex is (2, -3).

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