From Functions of Parabolas to Graphs of Parabolas
Intro
Not all graphs look like lines. In the next few days, we will look at another kind of graph. We will look at how to graph equations that have this type of function and we will also use functions to describe graphs that already exist.
So what type of graph am I talking about?
Problem 1: The Parabola Suspension Bridge
In the city of Metropolis, engineers are working feverishly to build a suspension bridge called The Parabola Suspension Bridge. The designs of the bridge include a function which describes the shape that the cables should take. The equation is y = x^2. (Note that the notation x^2 means x raised to the power of 2 - such a notation is used in most technologies such as your calculator)
With a partner, graph the equation y = x^2 using the same technique you used to graph lines. Create ordered pairs and connect the dots!
Acivity: Class Discussion
How does one graph the equation y = x^2?
Problem 2: Dr. Projec and the Flying Prism
Dr. Projec studies projectile motion in his physics lab. He has decided to launch a prism through the air, record it's travel with a video, and then use the video to create a graph. Dr. Projec puts a piece of paper up to the screen and draws a graph of the locations of the prism as it flies through the air. He describes his graph using the equation y = -x^2+5. Dr. Projec asks one of his colleagues, Motio, to draw a graph of the equation y = -x^2+5 so that he can compare the prism's flight to the equation y = x^2. Motio is quite lazy, and has asked for your help.
With a partner, graph the equation y = -x^2+5 using the same technique you used to graph lines. Do you get a shape similar to the graph produced from y = x^2?
Activity: Class Discussion
How does one graph the equation y = -x^2+5?
The Parabola
The graph is what is called a parabola. This graph is upside side because of the negative sign in front of the x^2. Can you guess which parabola is drawn above? It is the parabola y = x^2+2. Parabolas are shaped like the letter "U". Like a line, they expand infinitely on both side. When graphs have the shape of a parabola, they are called "Parabolic". Functions that make these graphs are called quadratic functions.
Reflection
What is a parabola? How does a quadratic function create a graph of a parabola? What have you learned?
Return Links
Unit 1 of Welcome to the Graphs of Life: Graphing Functions