Overview
On this page, we discuss how to graph quadratic parabolas, and piecewise linear functions.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Recall how to find the \(x\)- and \(y\)-intercepts and slope of a straight line, and draw its graph.
- Use the quadratic formula to find the \(x\)-intercepts of a parabola.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Find the coordinates of the vertex of a parabola, and determine which direction the parabola opens.
- Sketch the graph of a parabola from its \(x\)- and \(y\)-intercepts, its vertex, and the direction it opens.
- Draw the graph of a piecewise linear functions by combining the graphs of each of its constituent line segments and half-lines.
To prepare for class
-
Watch the following video (by Khan Academy) which reviews how to find the \(x\)- and \(y\)-intercepts of a line, and draw the graph:
-
Watch the following video (by Math Academy) which shows how to find the \(x\)-intercepts of a parabola from its equation, and vice-versa:
After class
-
Watch the following videos (by Tyler Wallace) which give examples of how to sketch the graph of a parabola:
-
Watch the following video (by Marty Brandl) which gives examples of how to sketch the graph of a piecewise linear function: