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Do Now

Do Now. Pass out the calcs .. Work on Practice EOC Week # 13 Block 4 ONLY: Pick up a homework answer key from the back table and correct your homework. Do yo thang. Do Now. Pass out the calcs .. Pick a homework answer from the table and correct your homework form last night.

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Do Now

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  1. Do Now • Pass out the calcs.. • Work on Practice EOC Week # 13 • Block 4 ONLY: Pick up a homework answer key from the back table and correct your homework. • Do yothang...

  2. Do Now • Pass out the calcs.. • Pick a homework answer from the table and correct your homework form last night. • Solve the following problem by completing the square. 4y2 + 4y - 7 = 0 • Do yo thing... Answer: -1.91, 0.91

  3. Do Now • Pass out the calcs.. • Hand your advertisement activity into the tray. • Work out the following TCAP question on a sheet of notebook paper. Write an explanation next to EACH answer as to why or not you chose that answer.

  4. Objective: • So solve quadratic equations using the QUADRATIC FORMULA!

  5. Quadratic Formula • To use this formula your equation must be in this form… ax2 + bx + c

  6. Quadratic Formula

  7. The FUN song… • http://spongebob.nick.com/videos/clip/promo-spongebash-fun-song.html

  8. 8 3 8 8 8 –1 and 1 and – 1 and –1 and – A B C D 3 3 3 –b b2 – 4ac ± x = 2a EXAMPLE 1 Standardized Test Practice What are the solutions of 3x2 + 5x = 8? SOLUTION 3x2 + 5x = 8 Write original equation. 3x2 + 5x – 8 = 0 Write in standard form. Quadratic formula

  9. 52 – 4(3)(–8) –5 ± 8 x = 2(3) 3 –5 121 ± = 6 –5 ± 11 = –5 – 11 and The solutions of the equation are 6 6 –5 + 11 = 1 6 – = ANSWER The correct answer isC. EXAMPLE 1 Standardized Test Practice Substitute values in the quadratic formula: a = 3, b = 5, andc =–8. Simplify. Simplify the square root.

  10. –b 2a b2 – 4ac x= ( –1)2 – 4(2)(–7) + – (–1) – = 2(2) 1 57 + + – – = 4 EXAMPLE 2 Solve a quadratic equation Solve 2x2 – 7 = x. 2x2– 7 = x Write original equation. 2x2–x – 7 = 0 Write in standard form. Quadratic formula Substitute values in the quadratic formula: a=2, b= –1, and c = –7. Simplify.

  11. 57 57 EXAMPLE 2 Solve a quadratic equation ANSWER The solutions are 1 + 1 – 2.14 and –1.64. 4 4 CHECK Write the equation in standard form, 2x2–x–7=0. Then graph the related function y=2x2–x–7. The x-intercepts are about –1.6 and 2.1. So, each solution checks.

  12. ANSWER ANSWER ANSWER 4 0.23, 1.43 0.25, 2 for Examples 1and 2 GUIDED PRACTICE Solve the equation by Quadratic Formula. 1. x2 – 8x+ 16 = 0 2. 3n2 – 5n = –1 3. 4z2 = 7z+ 2

  13. FILM PRODUCTION For the period 1971  2001, the number y of films produced in the world can be modeled by the functiony = 10x2  94x + 3900 wherexis the number of years since1971. In what year were 4200 films produced? EXAMPLE 3 Use the quadratic formula SOLUTION y =10x2– 94x+ 3900 Write function. 4200 = 10x2– 94x – 3900 Substitute 4200 for y. 0 = 10x2– 94x – 300 Write in standard form.

  14. (–94)2 – 4 (10)(–300) + –(–94) x = – 2(10) 20,836 94 = 20 20,836 94 – 20,836 94+ 12 –3. and 20 20 + There were 4200 films produced about 12 years after 1971, or in 1983. – ANSWER EXAMPLE 3 Use the quadratic formula Substitute values in the quadraticformula: a =10,b = –94, andc =–300. Simplify. The solutions of the equation are:

  15. Methods for Solving the Quadratic Formula… • Pg. 673

  16. EXAMPLE 4 Choose a solution method Tell what method you would use to solve the quadratic equation. Explain your choice(s). a. 10x2 – 7 = 0 SOLUTION a. The quadratic equation can be solved using square roots because the equation can be written in the form x2=d.

  17. EXAMPLE 4 Choose a solution method Tell what method you would use to solve the quadratic equation. Explain your choice(s). b.x2 + 4x = 0 SOLUTION b. The equation can be solved by factoring because the expression x2+4x can be factored easily. Also, the equation can be solved by completing the square because the equation is of the form ax2+bx+c=0 where a=1 and b is an even number.

  18. EXAMPLE 4 Choose a solution method Tell what method you would use to solve the quadratic equation. Explain your choice(s). c. 5x2 + 9x – 4 = 0 SOLUTION c. The quadratic equation cannot be factored easily, and completing the square will result in many fractions. So, the equation can be solved using the quadratic formula.

  19. for Example 4 GUIDED PRACTICE Tell what method you would use to solve the quadratic equation. Explain your choice(s). 5. x2 + x – 6 = 0 SOLUTION Factoring because the expression factors easily.

  20. for Example 4 GUIDED PRACTICE Tell what method you would use to solve the quadratic equation. Explain your choice(s). 6. x2 – 9 = 0 SOLUTION Factoring because the expression factors easily. Using square roots is another option since the equation can be written in the formx2 = d.

  21. for Example 4 GUIDED PRACTICE Tell what method you would use to solve the quadratic equation. Explain your choice(s). 7. x2 + 6x = 5 SOLUTION Completing the square because the equation is of the form ax2 + bx = c where a = 1 and b is an even number. Another method is the quadratic formula since the equation does not factor easily.

  22. Exit Ticket: What are the solutions to the following equations? • 2x2 + 7x = 9 • 3x2 – 1 = x How can you choose which method to you use finding the roots to an equation?

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