Graph a quadratic inequality

1
Graph a quadratic inequality
EXAMPLE 1
Graph y gt x2 3x 4.
SOLUTION
STEP 1
Graph y x2 3x 4. Because the inequality
symbol is gt, make the parabola dashed.
STEP 2
Test a point inside the parabola, such as (0, 0).
y gt x2 3x 4
0 gt 4
2
Graph a quadratic inequality
EXAMPLE 1
So, (0, 0) is a solution of the inequality.
STEP 3
Shade the region inside the parabola.
3
Use a quadratic inequality in real life
EXAMPLE 2
Rappelling
A manila rope used for rappelling down a cliff
can safely support a weight W (in pounds) provided
W 1480d2
where d is the ropes diameter (in inches).
Graph the inequality.
SOLUTION
Graph W 1480d2 for nonnegative values of d.
Because the inequality symbol is , make the
parabola solid. Test a point inside the parabola,
such as (1, 2000).
4
Use a quadratic inequality in real life
EXAMPLE 2
W 1480d2
Because (1, 2000) is not a solution, shade the
region below the parabola.
5
Graph a system of quadratic inequalities
EXAMPLE 3
Graph the system of quadratic inequalities.
y lt x2 4
Inequality 1
y gt x2 2x 3
Inequality 2
SOLUTION
STEP 1
Graph y x2 4. The graph is the red region
inside and including the parabola y x2 4.
6
Graph a system of quadratic inequalities
EXAMPLE 3
STEP 2
Graph y gt x2 2x 3. The graph is the blue
region inside (but not including) the parabola y
x2 2x 3.
STEP 3
Identify the purple region where the two graphs
overlap. This region is the graph of the system.
7
for Examples 1, 2, and 3
GUIDED PRACTICE
Graph the inequality.

y gt x2 2x 8
y lt 2x2 3x 1

8
for Examples 1, 2, and 3
GUIDED PRACTICE
Graph the inequality.

Graph the system of inequalities consisting of y
x2 and y lt x2 5.
y lt x2 4x 2