Rewrite f(x) = -(x + 3)² - 1 from vertex form to standard form.

Solution:

The vertex form of a quadratic function is given by f (x) = a(x - h)² + k,

Where (h, k) is the vertex of the parabola where a, h and k are real numbers and a ≠ 0.

Quadratic function in standard form is written in the form, f (x) = ax² + bx + c,

Where a, b and c are real numbers (constants) where a ≠ 0 and x and y are variables where (x, y) represents a point on the parabola.

Given that: f(x) = -(x + 3)² - 1 ,

Expanding the terms using the identity (a + b)² = a² + b² + 2ab,

f(x) = -x² - 6x - 9 - 1

f(x) = -x² - 6x - 10

Rewrite f(x) = -(x + 3)² - 1 from vertex form to standard form.

Summary:

The standard form of f(x) = -(x + 3)² - 1 is f(x) = -x² - 6x - 10.