To rewrite the quadratic function y = -9(x-1)²-6 in standard form, we need to expand the squared term and simplify the expression. Here are the steps:
Distribute the negative sign to the squared term: y = -9(x² - 2x + 1) - 6
Multiply -9 by each term inside the parentheses: y = -9x² + 18x - 9 - 6
Combine the constants: y = -9x² + 18x - 15
Therefore, the standard form of the quadratic function y = -9(x-1)²-6 is y = -9x² + 18x - 15.