Final answer:
The minimum value of f(x) = 2x²-16x+30 is 14.
Step-by-step explanation:
To find the minimum value of the quadratic function f(x) = 2x² - 16x + 30, we can use the formula for the vertex of a parabola, which is x = -b/2a. First, let's find the vertex x-coordinate: x = -(-16)/(2*2) = 4.
Next, substitute x = 4 into the original function to find the minimum value: f(4) = 2(4)² - 16(4) + 30 = 14. Therefore, the minimum value of f(x) is 14.