+
6-7
Graphing
and Solving
Quadratic
Inequalities
Objectives:
1) Graph Quadratic Inequalities in Two Variables.
2) Solve Quadratic Inequalities in One Variable.
+
Recall how to Graph Linear Inequalities:
y < -3x + 5
Graphing
Quadratic
Inequalities
+
You can graph quadratic inequalities in two variables using the
same techniques you used to graph linear inequalities in two variables.

Steps:
1)
Determine whether the boundary should be solid or dashed. Graph
the quadratic function.
2)
Test a point inside the parabola. Check to see if this ordered pair
is a solution to the inequality.
If the resulting
Inequality is TRUE,
shade INSIDE
the parabola.
If the resulting
inequality is FALSE,
shade OUTSIDE
your parabola
+ Example 1a:
Graph a Quadratic Inequality
Graph y < x2 -6x – 7
Methods to graph:
1)
Table of values.
2)
Find x-intercepts (zeros) and
vertex.
+ Example 1b:
Graph a Quadratic Inequality
Graph y > x2 - 4
+ Example 1c:
Graph a Quadratic Inequality
Graph y > - x2 + 10x - 25
+ Solving Quadratic Inequalities

To solve a quadratic inequality in one variable, you can use the
graph of the related quadratic function.

To solve ax2 + bx + c < 0, graph y = ax2 + bx + c. Identify the x
values for which the graph lies BELOW the x-axis.

To solve ax2 + bx + c > 0, graph y = ax2 + bx + c. Identify the x
values for which the graph lies ABOVE the x-axis.

For < or >, include the x-intercepts in the solution.
+ Example 2a:
Solve by Graphing.
 Solve
x2 + 2x – 3 > 0
+ Example 2b:
Solve by Graphing.
Solve –x2 – 10x – 21 < 0
+ Example 2c:
Solve by Graphing.
Solve x2 – 9 > 0
+
Solve Quadratic Inequalities
Algebraically
 Solve
the related equation to identify the
zeros.
 Plot
the zeros on a number line (be careful
with open vs. closed circles).
 Test
a value in each interval to see if it
satisfies the original inequality.
Example 3a:
+
Solve Algebraically
Solve x2 + x > 6
Example 3b:
+
Solve Algebraically
Solve x2 - 4x < 5
+
You Try It…

Solve the quadratic inequality algebraically.
9x < 12x2
+ Application

Vanessa has 180 feet of fencing that she intends to use to
build a rectangular play area for her dog. She wants the play
area to enclose at least 1800 square feet. What are the
possible widths of the play area?
+
Homework
Text p. 332-333 #s 1-8 all
Text p. 333 #s 9-13 all