Question

Write the function f(x) = (x - 6)^2 + 9 in standard form.

Answer 1

The standard form of the function f(x) = (x - 6)^2 + 9 is obtained by expanding the squared term and combining like terms, resulting in x^2 - 12x + 45.

Step-by-step explanation:

The function f(x) = (x - 6)^2 + 9 is already in vertex form. However, to write it in standard form, you need to expand the squared term and combine like terms. Here's how to do that step by step:

1. Expand the squared term: (x - 6)(x - 6) = x^2 - 12x + 36.
2. Add the constant term outside the parenthesis to the result: x^2 - 12x + 36 + 9.
3. Combine like terms to obtain the standard form: x^2 - 12x + 45.

The standard form of the given function f(x) is therefore x^2 - 12x + 45.