Unit 5, Lesson 5
How Many Solutions?
Integrated Math 2
Preparation
Lesson Narrative
The work in this lesson builds on the idea that both graphing and rewriting quadratic equations in a form with one side equal to zero are useful strategies for solving equations. It also reinforces the ties between the zeros of a function and the horizontal intercepts of its graph, which students began exploring in an earlier unit.
Students also explore some potential misconceptions, such as trying to use the zero product property when one side of the equation is not zero and dividing by a variable. As they explain why certain algebraic moves are acceptable and others are not, students practice constructing logical arguments (MP3).
- Coordinate (orally) graphs with no horizontal intercepts, quadratic functions with no (real) zeros, and quadratic equations with no (real) solutions.
- Describe (orally and in writing) the relationship between the solutions to quadratic equations of the form $\text {expression}=0$ and the horizontal intercepts of the graph of the related function.
- Explain (orally and in writing) why dividing each side of a quadratic equation by a variable is not a reliable way to solve the equation.