Question

The number of brand name shoes in stock at the beginning of month in a store follows a quadratic model. In January (t = 1), there are 36 pairs of shoes; in March (t = 3).there are 52 pairs, and in September, there are also 52 pairs. Which of the following quadratic models represent the number of pairs of shoes in stock?

Answer 1

This is an easy question to solve.

Once our function depends on "t", all we just need to do is to try different values of "t" for our function and than compare the values with the number of pairs of shoes for each value of "t". To illustrate it, let's calculate as follows:

We can see,

$f(t)=-t^2+12\cdot t+25$

satisfies what we need, so we do not need to try the other expressions, but if we do so, we will see that the other expressions do not satisfy what we need.

So the final answer is

$f(t)=-t^2+12\cdot t+25$