options: Interpret expressions for functions in terms of the situation they model.

Analyze functions using different representations.

Extend the domain of trigonometric functions using the unit circle.

Understand the concept of a function and use function notation.

Build new functions from existing functions.

Define, evaluate, and compare functions.

Use functions to model relationships between quantities.

Construct and compare linear and exponential models and solve problems.

Interpret functions that arise in applications in terms of the context.

Build a function that models a relationship between two quantities.

Model periodic phenomena with trigonometric functions.

Prove and apply trigonometric identities.
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?


correct_option_index: 1