In this lesson, students learn about the zero product property. They use it to reason about the solutions to quadratic equations that each have a quadratic expression in factored form on one side and 0 on the other side. They see that when an expression is a product of two or more factors and that product is 0, one of the factors must be 0. This fact enables us to find unknown values in the factored expression.
Students also continue to make connections to their earlier work on quadratic functions. They have seen that sometimes we want to find the input values of a function when the output is zero. They also learned that the factored form can help us identify the zeros of a quadratic function and the \(x\)-intercepts of its graph. They have not investigated how or why this form enables us to do so, however. Here, students make use of the structure of a quadratic expression in factored form and the zero product property to understand the connections between the numbers in the form and the \(x\)-intercepts of its graph (MP7).
- Given quadratic equations where one side is a product of factors and the other is zero, find the solution(s) and explain (orally and in writing) why the solutions make the equation true.
- Understand that the “zero product property” (in written and spoken language) means that if the product of two numbers is 0 then one of the factors must also be 0.
- Let’s find solutions to equations that contain products that equal zero.
- I can explain the meaning of the “zero product property.”
- I can find solutions to quadratic equations when one side is a product of factors and the other side is zero.
zero product property
The zero product property says that if the product of two numbers is 0, then one of the numbers must be 0.