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9.4 Solving Trinomials

9.4 Solving Trinomials. Steps. Move all terms to one side of the = Factor Set each factor equal to zero Solve each factor Check all answers. Solve. Original equation. Rewrite so one side equals 0. Factor the left side. or. Zero Product Property. Solve each equation.

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9.4 Solving Trinomials

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  1. 9.4 Solving Trinomials

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

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

  4. Solve Answer: Example 4-4b

  5. Model RocketsMs. 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 Example 4-5a

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

  7. The solutions are and seconds. 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. Example 4-5a Answer: 3.5 seconds

  8. 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 Example 4-5b

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

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

  11. Solve Check your solutions. Answer: Example 3-5b

  12. Example 3-6a ArchitectureMarion 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? Explore Begin by making a diagram like the one shown to the right, labeling the appropriate dimensions.

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

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

  15. PhotographyAdina 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? Answer: Example 3-6b

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

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