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Unit 1 Part B – Applications of Quadratics

Unit 1 Part B – Applications of Quadratics. By: Andrew, Lajanthan , Manpreet , Prabhakar , and Richard. Introduction. Radicals. Solving Systems of Equations Graphically. Solving Systems of Equations Algebraically. Quadratic Word Problems. Terminology.

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Unit 1 Part B – Applications of Quadratics

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  1. Unit 1 Part B – Applications of Quadratics By: Andrew, Lajanthan, Manpreet, Prabhakar, and Richard

  2. Introduction Radicals Solving Systems of Equations Graphically Solving Systems of Equations Algebraically Quadratic Word Problems

  3. Terminology Radicals – used to express exact numbers Linear System – 2 or more linear lines Linear-Quadratic System – at least one linear and one quadratic Solution (to a system of equations) – the point at which the lines intersect Quadratic Equation – used to find the x-intercepts Quadratic Function – used to find the maximum/minimum value of the dependent variable

  4. Simplifying Radicals

  5. Simplifying Radicals Radicals are used to express exact numbers The number under the square root sign is called the radicand Radicand

  6. Simplifying Radicals

  7. Adding/Subtracting Radicals

  8. Multiplying Radicals

  9. Dividing Radicals

  10. Dividing Radicals

  11. Try it yourself… a) b)

  12. Solving Linear-Quadratic Systems Graphically

  13. Solving Linear-Quadratic Systems Graphically A system of equations is two or more equations The point(s) at which the equations intersect is called the solution Linear Systems can have: • One solution • Two solutions • Infinite solutions Linear-Quadratic Systems can have: • No solutions • One solution • Two solutions You can solve a system by graphing it!

  14. Solving Linear-Quadratic Systems Graphically Solve the following system of equations graphically: y = 2x + 5 y = x2 + 5

  15. Therefore, the solutions to the system are (0, 5) and (2, 9)

  16. Try it yourself… Solve the following system graphically: y = 2(x+3) 2 y = -2x - 2 Therefore, the solutions to the system are (-2, 2) and (-5, 8)

  17. Solving Linear-Quadratic Systems Algebraically

  18. Solving Linear-Quadratic Systems Algebraically You can also solve a system of equations algebraically! Recall: Linear Systems can have: • No solutions • One solution • Infinite solutions Linear-Quadratic Systems can have: • No solutions • One solution • Two solutions

  19. Solving Linear-Quadratic Systems Algebraically Use the discriminant, b2 – 4ac, to find out how many solutions the system has • If b2 – 4ac > 0 then there are 2 solutions • If b2 – 4ac = 0 then there is 1 solution • If b2 – 4ac < 0 then there are no solutions If there are solutions to the system, solve them by using Substitution

  20. Solving Linear-Quadratic Systems Algebraically Solve the following system of equations algebraically: y = x2 - 21x + 9 y = 13x - 7 Therefore, the solution to this system is (4,-59) Check: y = x2 - 21x + 9 -59 = (4)2 – 21(4) + 9 -59 = -59

  21. Try it yourself… Solve the following system of equations algebraically: y = 3x2 - x +9 y = 2x + 3 There are no solutions to this system

  22. Quadratic Word Problems

  23. Quadratic Word Problems For the Athletic Banquet, the cafeteria averages the cost of one meal per person at 20 dollars. The venue is set for 100 people. The school says that for every 2 dollar increase in the ticket price, 3 people will not attend. What should be the price of a ticket if the school wants to maximize profits?

  24. Quadratic Word Problems

  25. Home FUN! • Complete the Unit 1 Part B Practice Question on myclass • Review the study sheet for Unit 2 Thank you for listening!

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