Final answer:
The coordinates of the vertex for the given function are (1, 7).
Step-by-step explanation:
The given function is f(x) = 2x² - 4x + 9. The coordinates of the vertex can be found by using the formula x = -b / (2a), where a and b are the coefficients of x² and x respectively. In this case, a = 2 and b = -4. Substituting these values into the formula, we have x = -(-4) / (2 * 2) = 4 / 4 = 1.
To find the y-coordinate of the vertex, substitute x = 1 back into the original function: f(1) = 2(1)² - 4(1) + 9 = 2 - 4 + 9 = 7.
Therefore, the coordinates of the vertex are (1, 7).