Question

Let f(x)= -x^2+4x+1. Find the function value when x=2, -4

Answer 1

`\begin{gathered} \text{Given} \\ f(x)=-x^2+4x+1 \end{gathered}`

Evaluate at x = 2

Substitute x for x = 2 on all of the terms in the function, then simplify

`\begin{gathered} f(x)=-x^2+4x+1^{} \\ f(2)=-(2)^2+4(2)+1 \\ f(2)=-(4)+8+1 \\ f(2)=-4+8+1 \\ f(2)=5 \end{gathered}`

Therefore, f(x) is equal to 5 if x = 2.

Evaluate at x = -4

`\begin{gathered} f(x)=-x^2+4x+1 \\ f(-4)=-(-4)^2+4(-4)+1 \\ f(-4)=-(16)-16+1 \\ f(-4)=-16-16+1 \\ f(-4)=-31 \end{gathered}`

Therefore, f(x) is equal to -31 if x = -4.