1. Lesson 1

1.11. Lesson 1 Summary

Mathematics 20-1 Module 3

Module 3: Quadratic Functions

 

Lesson 1 Summary

 

This is an image of a parabolic grid next to stars. 

Comstock/Thinkstock

 

In this lesson you investigated the following questions:

  • How do the values of a, p, and q affect the appearance and placement of the graph of the function y = a(x − p)2 + q?

  • What are the characteristics of quadratic functions and their graphs?

You studied a specific form of the quadratic function, the vertex form. A quadratic function has a variable raised to the second power—in other words, squared. You learned that the graph of the function a(x − p)2 + q forms a parabolic shape. You discovered the effect of the variables a, p, and q on the shape of the parabola.

 

You saw that a affects the shape and orientation of the parabola. The farther a is from 0, the narrower the parabola. The orientation of the parabola is also affected by a in the way summarized in the table.

 

Direction of Opening If a > 0, the parabola opens upward. This sketch shows a parabola opening upward. A label states that a is greater than zero.
If a < 0, the parabola opens downward. This sketch shows a parabola opening upward. A label states that a is less than zero.


The variable p determines where the parabola is on the x-axis, and q determines where the parabola is on the y-axis.

 

This is a play button that opens Summary of Common Characteristics of Quadratic Functions.

The parabolic shape and other terms described during this lesson are summarized in Summary of Common Characteristics of Quadratic Functions.



In the next lesson you will investigate how to determine the coordinates of the vertex of a quadratic formula and how to accurately sketch the graph. You will learn how to determine the x- and y-intercepts of the graph and write a quadratic equation from a graph.