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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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For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

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