Final answer:
To find the vertex of the function 2x²-16x+33, use the formula x = -b/2a. In this case, the vertex is (4, 1).
Step-by-step explanation:
To find the vertex of the function 2x²-16x+33, we can use the formula x = -b/2a. In this case, a = 2 and b = -16. Plugging these values into the formula, we get x = -(-16)/2(2) = 16/4 = 4.
To find the y-coordinate of the vertex, we substitute the x-value back into the original function: f(4) = 2(4)² - 16(4) + 33 = 2(16) - 64 + 33 = 32 - 64 + 33 = 1.
Therefore, the vertex of the function 2x²-16x+33 is (4, 1).