1. 9.4 Solving Trinomials

2. Steps Move all terms to one side of the = Move all terms to one side of the = Factor Factor Set each factor equal to zero Set each factor equal to zero Solve each factor Solve each factor Check all answers Check all answers

3. Example 4-4a Solve Original equation Rewrite so one side equals 0. Factor the left side. orZero Product Property Solve each equation. Answer: The solution set is

4. Example 4-4b Solve Answer:

5. Example 4-5a Model Rockets Ms. Nguyen’s science class built an air-launched model rocket for a competition. When they test-launched their rocket outside the classroom, the rocket landed in a nearby tree. If the launch pad was 2 feet above the ground, the initial velocity of the rocket was 64 feet per second, and the rocket landed 30 feet above the ground, how long was the rocket in flight? Use the equation

6. Example 4-5a Vertical motion model Subtract 30 from each side. Factor out –4. Divide each side by –4. Factor orZero Product Property Solve each equation.

7. Example 4-5a The solutions areandseconds. The first time represents how long it takes the rocket to reach a height of 30 feet on its way up. The second time represents how long it will take for the rocket to reach the height of 30 feet again on its way down. Thus the rocket will be in flight for 3.5 seconds before coming down again. Answer: 3.5 seconds

8. Example 4-5b When Mario jumps over a hurdle, his feet leave the ground traveling at an initial upward velocity of 12 feet per second. Find the time t in seconds it takes for Mario’s feet to reach the ground again. Use the equation Answer: second

9. Example 3-5a SolveCheck your solutions. Original equation Rewrite the equation so that one side equals 0. Factor. or Zero Product Property Solve each equation. Answer: The solution is

10. Example 3-5a Check Substitute –5 and 3 for x in the original equation.

11. Example 3-5b SolveCheck your solutions. Answer:

12. Example 3-6a Architecture Marion has a small art studio measuring 10 feet by 12 feet in her backyard. She wants to build a new studio that has three times the area of the old studio by increasing the length and width by the same amount. What will be the dimensions of the new studio? ExploreBegin by making a diagram like the one shown to the right, labeling the appropriate dimensions.

13. Example 3-6a PlanLetthe amount added to each dimension of the studio. The new length times the new width equals the new area. old area Solve Write the equation. Multiply. Subtract 360 from each side.

14. Example 3-6a Factor. Solve each equation. Zero Product Property or ExamineThe solution set isOnly 8 is a valid solution, since dimensions cannot be negative. Answer: The length of the new studio should be or 20 feet and the new width should be or 18 feet.

15. Photography Adina has a photograph. She wants to enlarge the photograph by increasing the length and width by the same amount. What dimensions of the enlarged photograph will be twice the area of the original photograph? Example 3-6b Answer:

16. Practice Problems Page 499 Problems 14-27, 35-46