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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...

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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. 4y 2 + 4y - 7 = 0 Do yo thing... Answer: -1.91, 0.91

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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.

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Objective: So solve quadratic equations using the QUADRATIC FORMULA!

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Quadratic Formula To use this formula your equation must be in this form… ax 2 + bx + c

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Quadratic Formula

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EXAMPLE 1 Standardized Test Practice What are the solutions of 3x 2 + 5x = 8? –1 and – A 8 3 B –1 and 8 3 C 1 and – 8 3 D 1 and 8 3 SOLUTION Write original equation. 3x 2 + 5x = 8 Write in standard form. 3x 2 + 5x – 8 = 0 Quadratic formula ± x = –bb2 – 4ac 2a2a

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

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EXAMPLE 2 Solve a quadratic equation 2x 2 – 7 = x 2x 2 – x – 7 = 0 Solve 2x 2 – 7 = x. Write original equation. Write in standard form. Quadratic formula x =x = b 2 – 4ac + – –b 2a2a Substitute values in the quadratic formula: a = 2, b = –1, and c = –7. Simplify. – (–1) – + ( –1)2 – 4(2)(–7) 2(2) = 4 = + – 1 57

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

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

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EXAMPLE 3 Use the quadratic formula y = 10x 2 – 94x + 3900 4200 = 10x 2 – 94x – 3900 0 = 10x 2 – 94x – 300 Write function. Substitute 4200 for y. Write in standard form. SOLUTION For the period 1971 2001, the number y of films produced in the world can be modeled by the function y = 10x 2 94x + 3900 where x is the number of years since 1971. In what year were 4200 films produced ? FILM PRODUCTION

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

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Methods for Solving the Quadratic Formula… Pg. 673

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EXAMPLE 4 Choose a solution method Tell what method you would use to solve the quadratic equation. Explain your choice(s). a. 10x 2 – 7 = 0 SOLUTION a. The quadratic equation can be solved using square roots because the equation can be written in the form x 2 = d.

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Choose a solution method EXAMPLE 4 b. The equation can be solved by factoring because the expression x 2 + 4x can be factored easily. Also, the equation can be solved by completing the square because the equation is of the form ax 2 + bx + c = 0 where a = 1 and b is an even number. Tell what method you would use to solve the quadratic equation. Explain your choice(s). b. x 2 + 4x = 0 SOLUTION

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Choose a solution method EXAMPLE 4 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. Tell what method you would use to solve the quadratic equation. Explain your choice(s). c. 5x 2 + 9x – 4 = 0 SOLUTION

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GUIDED PRACTICE for Example 4 Tell what method you would use to solve the quadratic equation. Explain your choice(s). SOLUTION Factoring because the expression factors easily. 5. x 2 + x – 6 = 0

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GUIDED PRACTICE for Example 4 Tell what method you would use to solve the quadratic equation. Explain your choice(s). SOLUTION Factoring because the expression factors easily. Using square roots is another option since the equation can be written in the form x 2 = d. 6. x 2 – 9 = 0

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GUIDED PRACTICE for Example 4 Tell what method you would use to solve the quadratic equation. Explain your choice(s). SOLUTION Completing the square because the equation is of the form ax 2 + bx = c where a = 1 and b is an even number. Another method is the quadratic formula since the equation does not factor easily. 7. x 2 + 6x = 5

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Exit Ticket: What are the solutions to the following equations? 1.2x 2 + 7x = 9 2.3x 2 – 1 = x How can you choose which method to you use finding the roots to an equation?

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