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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

Graph a quadratic inequality

EXAMPLE 1

So, (0, 0) is a solution of the inequality.

STEP 3

Shade the region inside the parabola.

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).

Use a quadratic inequality in real life

EXAMPLE 2

W 1480d2

Because (1, 2000) is not a solution, shade the

region below the parabola.

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.

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.

for Examples 1, 2, and 3

GUIDED PRACTICE

Graph the inequality.

y gt x2 2x 8

y lt 2x2 3x 1

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

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