Final answer:
To rewrite the quadratic function y = -3/6x² + 1/2x - 8 in the form y = a(x - h)² + k, you need to complete the square.
Step-by-step explanation:
To rewrite the quadratic function y = -3/6x² + 1/2x - 8 in the form y = a(x - h)² + k, we need to complete the square. First, let's factor out the common factor of -1/6 from the quadratic term: y = (-1/6)(x² - (1/3)x) - 8. Now, let's complete the square by adding and subtracting the square of half the coefficient of x: y = (-1/6)(x² - (1/3)x + (1/6)² - (1/6)²) - 8. Simplifying the expression inside the parentheses, we get: y = (-1/6)((x - 1/6)² - 1/36) - 8. Expanding and simplifying further, we get: y = (-1/6)(x - 1/6)² + 1/216 - 48/6. Finally, combining like terms, we get: y = (-1/6)(x - 1/6)² - 287/216. Therefore, the quadratic function y = -3/6x² + 1/2x - 8 can be rewritten in the form y = (-1/6)(x - 1/6)² - 287/216.