High School

Given the polynomial function below, find [tex]F(-5)[/tex].

[tex]f(x) = x^2 - 2x - 7[/tex]

A. -42
B. 8
C. -22
D. 28

Answer :

To find the value of the function at $x = -5$, substitute $-5$ into the polynomial function

$$
f(x) = x^2 - 2x - 7.
$$

Step 1: Substitute $x = -5$ into the function:

$$
f(-5) = (-5)^2 - 2(-5) - 7.
$$

Step 2: Calculate the square term:

$$
(-5)^2 = 25.
$$

Step 3: Evaluate the linear term:

$$
-2(-5) = 10.
$$

Step 4: Combine the constant term along with the results:

$$
f(-5) = 25 + 10 - 7.
$$

Step 5: Sum the numbers:

$$
25 + 10 = 35, \quad \text{and} \quad 35 - 7 = 28.
$$

Thus,

$$
f(-5) = 28.
$$

The final answer is $\boxed{28}$.