Solving Quadratic Equations with the Zero Product Property
Integrated Math 2
4.1
Warm-up
What values of the variables make each equation true?
4.2
Activity
For each equation, find its solution or solutions. Be prepared to explain your reasoning.
4.3
Activity
We have seen quadratic functions modeling the height of a projectile as a function of time.
Here are two ways to define the same function that approximates the height of a projectile in meters, seconds after launch:
Which way of defining the function allows us to use the zero product property to find out when the height of the object is 0 meters?
Without graphing, determine at what time the height of the object is 0 meters. Show your reasoning.
Student Lesson Summary
The zero product property says that if the product of two numbers is 0, then one of the numbers must be 0. In other words, if then either or . This property is handy when an equation we want to solve states that the product of two factors is 0.
Suppose we want to solve . This equation says that the product of and is 0. For this to be true, either or , so both 0 and -9 are solutions.
Here is another equation: . The equation says the product of and is 0, so we can use the zero product property to help us find the values of . For the equation to be true, one of the factors must be 0.
For to be true, would have to be 2.345.
For or () to be true, would have to be , or .
The solutions are 2.345 and .
In general, when a quadraticexpression in factored form is on one side of an equation and 0 is on the other side, we can use the zero product property to find its solutions.
This property is unique to 0. Given an equation like , the factors could be 2 and 3, 1 and 6, -12 and , and , or any other of the infinite number of combinations. This type of equation does not give insight into the value of or .
The zero product property says that if the product of two numbers is 0, then one of the numbers must be 0.
