Algebra I | Unit 1 2 3 4 5 6 7
In this unit, students learn about quadratic functions. Earlier, they learned about linear functions that grow by repeatedly adding or subtracting the same amount and exponential functions that grow by repeatedly multiplying by the same amount.
Quadratic functions also change in a predictable way. Here, the number of small squares in each step is increasing by 3, then 5, then 7, and so on. How many squares are in Step 10? How many in Step nn?
Here is a table that shows the pattern.
In this unit, students will also learn about some real-world situations that can be modeled by quadratic functions. For example, when you toss a ball up in the air, its distance above the ground as time passes can be modeled by a quadratic function. Study the graph. The ball starts on the ground because the height is 0 when time is 0. The ball lands back on the ground after 2 seconds. After 1 second, the ball is 5 meters in the air.
Both of the following expressions give the ball’s distance above the ground: 5x(2−x)5x(2−x) and 10x−5x210x−5x2, where xx represents the number of seconds since it was thrown. Quadratic expressions are most recognizable when you can see the “squared term,” -5x2-5x2, as shown in 10x−5x210x−5x2
Your student will learn more about quadratics in the next unit.
The equation h=1+25t2−5t2h=1+25t2−5t2 models the height in meters of a model rocket tt seconds after it is launched in the air. Here is a graph representing the equation.
IM Algebra 1 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).