Quadratic Inequalities (Equations and Parabolas)
Solving a Quadratic Inequality Graphically
The graph of a quadratic function in a Cartesian coordinate system is a parabola.
To solve a quadratic inequality or graphically, draw the corresponding parabola, then:
- The x-coordinates of the points (if they exist) where the parabola intersects the x-axis are the solution of the equation (zeros of the equation)
- The x-coordinates of the points (if they exist) where the parabola is above the x-axis are solution of the inequality
- The x-coordinates of the points (if they exist) where the parabola is below the x-axis are solution of the inequality
Ready, Set, Practice!
Find the solutions of a quadratic equation or inequality by exploring the graph of the corresponding parabola.
Use the input box to enter different quadratic expressions and the drop down list to select the equation or inequality form to solve.
Use the mouse wheel or the predefined gestures for mobile devices to zoom in/out and view details in the Graphics View.
Today You Are the Teacher!
Today's assignment is the inequality .
Alice solves it like this: .
Bob solves first, and gets . Then he graphs the parabola corresponding to the given equation and finds the solution 
.
Chuck uses ChatGPT 2 and finds that the solution is .
Alice says that her method is faster than Bob's, because it doesn't require sketching a graph.
Grade your students' solutions, and explain the reasons for your grading.
Hamletic Doubt...
Below you can see the solution of one of the following inequalities.
Choose the correct one.
