Question

a company uses the given quadratic function to model its profits, in thousands of dollars, where x is the number of years since 2006.
$f(x) = -18x^2 + 202.61x + 1,282.46$
based on the model, what is $f(14)$, in thousands of dollars?

Explanation:

Step1: Substitute x = 14 into the function

We have the function \( f(x) = -18x^2 + 202.61x + 1282.46 \). Substitute \( x = 14 \) into it:
\( f(14) = -18\times(14)^2 + 202.61\times14 + 1282.46 \)

Step2: Calculate each term

First, calculate \( (14)^2 = 196 \), then \( -18\times196 = -3528 \)
Next, \( 202.61\times14 = 2836.54 \)

Step3: Sum the terms

Now, sum the three terms: \( -3528 + 2836.54 + 1282.46 \)
First, \( -3528 + 2836.54 = -691.46 \)
Then, \( -691.46 + 1282.46 = 591 \)

Answer:

591