9/26/2017

1

Quadratic Inequality in Two Variables: can be written in the form –

� < ��� + �� + �, � > ��� + �� + �,

� ≤ ��� + �� + �, � ≥ ��� + �� + �,

9/26/2017

2

Graph each of the quadratic inequalities.

1. � > −�� − 4� 2. � ≤ 2�� − 3� + 1

3. A computer desk with a solid glass top can safely support a weight W (in pounds) provided � ≤ 250��, where x is the thickness of the desktop (in inches). Graph the inequality.

9/26/2017

3

Graph each system of inequalities.

4. � ≤ −�� + 4 5. � > �� − 3

� > �� − 2� − 3 � ≤ −2�� + 4� + 2

Quadratic Inequality in One Variable: can be written in the form –

��� + �� + � < 0, ��� + �� + � > 0,

��� + �� + � ≤ 0, ��� + �� + � ≥ 0,

Example:

6. Solve �

��� + 3� − 2 < 0

9/26/2017

4

Solve each inequality algebraically.

7. �� − 2� > 15 8. 3�� − 9� − 12 < 0

9. The number T of teams that have participated in a robot-building competition for high school students can be modeled by � � = 7.51�� − 16.4� + 35.0, where x is the number of years since 1992. When was the first year that at least 300 teams participated in the robot-building competition.

9/26/2017

5

I give the graph, you write the function for it!!

Write the quadratic function for the parabolas shown.

1. 2.

9/26/2017

6

Write a quadratic function whose graph has the given characteristics.

3. vertex: (4,-5) 4. x-intercepts: -2, 5

passes through: (2,-1) passes through: (6,2)

Write a quadratic function in standard form for the parabola that passes through:

5. (-2,30), (1,6), and (4,36). 6. (-1,5), (0,-1), (2,11)

9/26/2017

7

Best Fitting Quadratic Model: quadratic regression; using a graphing calculator to get a quadratic regression.

7. A pumpkin tossing contest is held each year in Morton, Illinois, where people compete to see whose catapult will send pumpkins the farthest. One catapult launches pumpkins from 25 feet above the ground at a speed of 125 feet per second. The table shows the horizontal distances (in feet) the pumpkins travel when launched at different angles. Use a graphing calculator to find the best-fitting quadratic model for the data.