Question

Convert the following quadratic function to standard form.
f(x) = -2(x + 5)² - 8

Answer 1

The quadratic function f(x) = -2(x + 5)² - 8 is converted to standard form by expanding the squared term, distributing the -2, and combining like terms to get -2x² - 20x - 58.

Step-by-step explanation:

To convert the following quadratic function to standard form:

f(x) = -2(x + 5)² - 8

The first step is to recognize that this equation is already in what is called vertex form, which is given by f(x) = a(x - h)² + k, where (h,k) is the vertex of the parabola. In the standard form, the quadratic equation is written as ax² + bx + c. To convert from vertex to standard form, you need to expand the squared term and simplify.

Here is the step-by-step expansion:

1. Expand the square in the equation: f(x) = -2(x + 5)(x + 5) - 8
2. Multiply out the binomials: f(x) = -2(x² + 10x + 25) - 8
3. Distribute the -2 across the binomial: f(x) = -2x² - 20x - 50 - 8
4. Combine like terms: f(x) = -2x² - 20x - 58

Therefore, the quadratic function in standard form is -2x² - 20x - 58.