Final answer:
To rewrite the quadratic function in vertex form, use the formula y = a(x - h)² + k. In this case, the quadratic function is y = 8x² - 144x + 640. The coefficients can be used to find the vertex, which is (h, k). Plugging in the values, the quadratic function in vertex form is y = 8(x - 9)² - 784. Option a is correct.
Step-by-step explanation:
To rewrite the quadratic function in vertex form, we use the formula y = a(x - h)² + k, where (h, k) is the vertex. In this case, the coefficient of x² is 8, so a = 8. To find the vertex, we need to use the formula h = -b / (2a) and k = f(h), where f(h) is the value of y when x = h. Plugging in the values b = -144 and a = 8 into the formulas, we find h = 9 and k = -784. Therefore, the quadratic function in vertex form is y = 8(x - 9)² - 784. So, option a is the correct answer.