standard_description: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
problem_activity: Problem 1
A business is marketing its product and has collected data on sales and prices for the past few years. The company, through careful modeling, has determined that their profit is dependent upon the selling price of the item and that it follows a quadratic model.
The function below describes the profit,
$$P$$
, dependent upon the selling price,
$$s$$
, of its product.
$$P(s)=-20s^2+1,400s-12,000$$
a.  Write the function in intercept form and identify the roots.
b.  Explain what the roots mean in context of the situation.
c.  Write the function in vertex form and identify the vertex.
d.  Explain what the vertex means in context of the situation.
Problem 2
The height,
$$h$$
, in feet, of a projectile launched upward from a bridge is given by
$$ h=-16t^2+16t+96$$
, where
$$t$$
is time in seconds.
Write the equation in vertex form.
How long does it take for the projectile to reach maximum height?
What is the maximum height of the projectile?


aligns: no