Final answer:
To write the given quadratic function in standard form, expand the square and simplify.
Step-by-step explanation:
The given quadratic function is f(x) = -4(x-2)²-2. To write it in standard form, we need to expand the square and simplify.
Expanding (x-2)², we get (x-2)(x-2) = x² - 4x + 4.
Substituting this back into the original function, we get f(x) = -4(x-2)²-2 = -4(x² - 4x + 4) -2 = -4x² + 16x - 14. This is the quadratic function in standard form.