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Objective The student will be able to: use the zero product property to solve quadratic equations SOL: A.14 Designed by Skip Tyler, Varina High School Edited by R. Renka

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What is a quadratic equation? A second degree polynomial Why is it called quadratic? –Come from the Latin word quadratum meaning square

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On your graphing calculator go to the graph menu and type in the equation Check your view window (SHIFT F3) make sure your mins and -10 and your maxs are 10 Push DRAW or F6 to draw the function Where does the function cross the x-axis?

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To view the x,y table for this function: –Go back to the main menu –Go into the table menu –Push F6 for TABLE –You can type in values for x or use the arrow key –This will show you where the y-value for the function is zero i.e. the zeros of the function

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3 different ways to say the same thing 1.Zeros of the function (SOL way) 2.Roots of a function (old people way) 3.X-intercepts of a function (the only one that makes sense!)

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How to fund the zeros of a function without graphing it You will need to use the Zero product property (on next slide)

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Zero Product Property If a b = 0 then a=0, b=0, or both a and b equal 0.

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Using the Zero Product Property, you know that either x + 3 = 0 or x - 5 = 0 Solve each equation. x = -3 or x = 5 {-3, 5} 1. Solve (x + 3)(x - 5) = 0

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2. Solve (2a + 4)(a + 7) = 0 2a + 4 = 0 or a + 7 = 0 2a = -4 or a = -7 a = -2 or a = -7 {-2, -7}

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3. Solve (3t + 5)(t - 3) = 0 3t + 5 = 0 or t - 3 = 0 3t = -5 or t = 3 t = -5/3 or t = 3 {-5/3, 3}

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Solve (y – 3)(2y + 6) = 0 1.{-3, 3} 2.{-3, 6} 3.{3, 6} 4.{3, -6}

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1.Set the equation equal to 0. 2.Factor the equation. 3.Set each part equal to 0 and solve. 4.Check your answer on the calculator. 4 steps for solving a quadratic equation Set = 0 Factor Split/Solve Check

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4. Solve x 2 - 11x = 0 GCF = x x(x - 11) = 0 x = 0 or x - 11 = 0 x = 0 or x = 11 {0, 11} Set = 0 Factor Split/Solve Check

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5. Solve. -24a +144 = -a 2 Put it in descending order. a 2 - 24a + 144 = 0 (a - 12) 2 = 0 a - 12 = 0 a = 12 {12} Set = 0 Factor Split/Solve Check

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6. Solve 4m 2 + 25 = 20m 4m 2 - 20m + 25 = 0 (2m - 5) 2 = 0 2m - 5 = 0 2m = 5 m = Set = 0 Factor Split/Solve Check

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7. Solve x 3 + 2x 2 = 15x Set = 0 Factor Split/Solve Check x 3 + 2x 2 - 15x = 0 x(x 2 + 2x - 15) = 0 x(x + 5)(x - 3) = 0 x = 0 or x + 5 = 0 or x - 3 = 0 {0, -5, 3}

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Solve a 2 – 3a = 40 1.{-8, 5} 2.{-5, 8} 3.{-8, -5} 4.{5, 8}

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Solve 4r 3 – 16r = 0 1.{-16, 4} 2.{-4, 16} 3.{0, 2} 4.{0, 4} 5.{-2, 0, 2} The degree will tell you how many answers you have!

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Maria told this puzzle to her friends. “The product of four times my age and 45 less than three times my age is zero. How old am I?” Find Maria’s age. Let m = Maria’s age. 4m(3m - 45) = 0 4m = 0 or 3m - 45 = 0 m = 0 or 3m = 45 m = 0 or m = 15 0 is not reasonable so Maria is 15 years old !!

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Find two consecutive integers whose product is 240. Let n = 1st integer. Let n + 1 = 2nd integer. n(n + 1) = 240 n 2 + n = 240 n 2 + n – 240 = 0 (n – 15)(n + 16) = 0 Set = 0 Factor Split/Solve Check

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(n – 15)(n + 16) = 0 n – 15 = 0 or n + 16 = 0 n = 15 or n = -16 The consecutive integers are 15, 16 or -16, -15.

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Mrs. Navickas Algebraically: 1 Solve for y, if necessary. If equation is given equal to zero or a y is not present, rewrite in descending powers of x.

Mrs. Navickas Algebraically: 1 Solve for y, if necessary. If equation is given equal to zero or a y is not present, rewrite in descending powers of x.

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