Question

Rewrite F(x)= -x^2-4x+1 into the form f(x)=a(x-h)^2+k

Answer 1

To rewrite F(x) = -x^2 - 4x + 1 into the form f(x) = a(x - h)^2 + k, you need to complete the square.

The rewritten form is f(x) = -(x + 2)^2 + 5.

Step-by-step explanation:

Let's go step by step:

1. First, factor out the coefficient of x^2:
   • F(x) = -1(x^2 + 4x) + 1
2. Next, complete the square by adding and subtracting the square of half the coefficient of x:
   • F(x) = -1(x^2 + 4x + (4/2)^2 - (4/2)^2) + 1
3. Simplify the expression inside the parentheses:
   • F(x) = -1((x + 2)^2 - 4) + 1
4. Distribute the -1:
   • F(x) = -(x + 2)^2 + 4 + 1
5. Combine like terms:

• f(x) = -(x + 2)^2 + 5

Therefore, the rewritten form of F(x) = -x^2 - 4x + 1 is f(x) = -(x + 2)^2 + 5.