Sketching Quadratic Equations by hand…NO CALCULATOR 1.Decide if the parabola opens up or down. – Max or min? 2.Find the vertex. 3.Calculate the discriminant to know how many zeros the function has. – 0? 1? 2? – If 1 or 2 use C.T.S., F., or Q.F. to find zeros 4.If no zeros, plug a number less than your max/min AND a number greater than your max/min to find at least 2 more points on the graph. 5.Plot your points and sketch in the graph. – Should the line be solid or dotted?

Practice Vertex: Zeros: Points where it crosses the y-axis:

Practice Vertex: Zeros: Points where it crosses the y-axis:

5.8 Solving Quadratic Inequalities

Two-Variable Quadratic Inequalities

Sketching Quadratic Inequalities by hand…NO CALCULATOR 1.Follow all the steps for graphing a quadratic equation by hand. 2.Choose a point outside the parabola to test. – If statement is true shade outside the parabola – If statement is false move on to step 7. 3.Choose a point inside the parabola to test. – If statement is true shade inside the parabola

Important Information Opens up/down?# of zeros? Maximum/Minimum?Actual zeros? Vertex?Other points on the graph? Discriminant?Where to shade? Solid Line?Dotted Line?

Practice Vertex: Zeros: Points where it crosses the y-axis: Test Point Outside: Test Point Inside:

Practice Vertex: Zeros: Points where it crosses the y-axis: Test Point Outside: Test Point Inside:

Sketching Quadratic Inequalities Using Your Calculator 1.Graph the related equation using your calculator 2.Decide if the parabola opens up or down. – Max or min? 3.Find the max or min. 4.Find the zeros if the graph crosses the x-axis. 5.If no zeros, trace to the left of the max/min until you get a “good” point, then do the same to the right. 6.Plot your points and sketch in the graph. – Should your line be solid or dotted? 7.Choose a point outside the parabola to test. – If statement is true shade outside the parabola – If statement is false move on to step 7. 8.Choose a point inside the parabola to test. – If statement is true shade inside the parabola

Practice Vertex: Zeros: Points where it crosses the y-axis: Test Point Outside: Test Point Inside:

Practice Vertex: Zeros: Points where it crosses the y-axis: Test Point Outside: Test Point Inside: