Given the function $f (x) = 6 x^{2} - 3 x + 1$ . Calculate the following values:
$\begin{array}{l} f (- 2) = \\ f (- 1) = \\ f (0) = \\ f (1) = \\ f (2) = \end{array}$

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $\begin{array}{l} f (- 2) = 31 \\ f (- 1) = 10 \\ f (0) = 1 \\ f (1) = 4 \\ f (2) = 19 \end{array}$

Steps

Step 1 ：Given the function $f (x) = 6 x^{2} - 3 x + 1$ . We need to substitute the given x values into the function and calculate the result.

Step 2 ：For $f (- 2)$ , substitute $- 2$ into the function to get $6 (- 2)^{2} - 3 (- 2) + 1 = 24 + 6 + 1 = 31$ .

Step 3 ：For $f (- 1)$ , substitute $- 1$ into the function to get $6 (- 1)^{2} - 3 (- 1) + 1 = 6 + 3 + 1 = 10$ .

Step 4 ：For $f (0)$ , substitute $0$ into the function to get $6 (0)^{2} - 3 (0) + 1 = 0 + 0 + 1 = 1$ .

Step 5 ：For $f (1)$ , substitute $1$ into the function to get $6 (1)^{2} - 3 (1) + 1 = 6 - 3 + 1 = 4$ .

Step 6 ：For $f (2)$ , substitute $2$ into the function to get $6 (2)^{2} - 3 (2) + 1 = 24 - 6 + 1 = 19$ .

Step 7 ：Final Answer: $\begin{array}{l} f (- 2) = 31 \\ f (- 1) = 10 \\ f (0) = 1 \\ f (1) = 4 \\ f (2) = 19 \end{array}$