In the previous two lessons, students analyzed quadratic functions that modeled projectile motion. In this lesson, they encounter a quadratic relationship in an economic context. They use a table of values to study the relationship between price and revenue, write an equation to define the function, and consider what the graph of the function tells us about the situation being modeled. In building a quadratic function to solve a pricing problem, students engage in aspects of modeling (MP4).
Students also deepen their understanding of the zeros and the domain of a quadratic function, and of the vertex of its graph. They interpret these features in various contexts, reasoning concretely and abstractly (MP2).
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. Consider making technology available, in case requested.
- Choose an appropriate domain for a quadratic function representing a context and explain (orally) the reasoning why it was selected.
- Interpret (orally and in writing) the vertex of a graph and the zeros of a quadratic function in context.
- Write and graph equations to model economic situations characterized by quadratic functions.
- Let’s look at how to maximize revenue.
- I can choose a domain that makes sense in a revenue situation.
- I can model revenue with quadratic functions and graphs.
- I can relate the vertex of a graph and the zeros of a function to a revenue situation.
A function where the output is given by a quadratic expression in the input.
vertex (of a graph)
The vertex of the graph of a quadratic function or of an absolute value function is the point where the graph changes from increasing to decreasing or vice versa. It is the highest or lowest point on the graph.
zero (of a function)
A zero of a function is an input that yields an output of zero. If other words, if \(f(a) = 0\) then \(a\) is a zero of \(f\).