Question

F(x)=x^2+2x+26
Rewrite function by completing the square
f(x)=(x+__)^2+___

Answer 1

The function f(x) = x^2 + 2x + 26 can be rewritten as f(x) = (x + 1)^2 + 25 by completing the square.

Explanation:

To rewrite the function f(x) = x^2 + 2x + 26 by completing the square, we follow these steps:

1. Take half of the coefficient of x, which is 1/2(2) = 1.

2. Square the result of step 1, which is 1^2 = 1.

3. Add and subtract the result of step 2 inside the parentheses, like this:

f(x) = x^2 + 2x + 1 - 1 + 26

Rearrange the terms inside the parentheses:

f(x) = (x + 1)^2 + 25

Therefore, the function f(x) = x^2 + 2x + 26 can be rewritten as f(x) = (x + 1)^2 + 25 by completing the square.