# Quadratic Inequalities (Equations and Parabolas)

## Solving a Quadratic Inequality Graphically

The graph of a

*in a Cartesian coordinate system is a***quadratic function***. To***parabola***a***solve***or***quadratic inequality***, draw the corresponding parabola, then:***graphically**- The
of the points (if they exist) where the**x-coordinates**the**parabola intersects**are the**x-axis**of the**solution**(zeros of the equation)**equation**

- The
of the points (if they exist) where the**x-coordinates**is**parabola**the**above**are**x-axis**of the**solution****inequality**

- The
of the points (if they exist) where the**x-coordinates**is**parabola**the**below**are**x-axis**of the*solution***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.