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U4-S3-L3 Solve Quadratics by Square Roots Essential Question: How do you solve a quadratic equation by graphing and square roots?

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Solving To solve a quadratic function, look for the x- intercepts: where the parabola intersects the x-axis. Words for solutions to quadratics: 1) zeros Words for solutions to quadratics: 1) zeros 2) roots 2) roots 3) solutions 3) solutions 4) answers 4) answers 5) x-intercepts 5) x-intercepts

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Solutions A zero is just like looking for an x-intercept A quadratic will only have 2, 1, or no zeros.

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Solving by Graphing

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Practice 1) x 2 - 9 = 02) -½ x 2 + 1 = 0

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Main Idea Some quadratic equations are missing an a, b, or c value, and graphing can be difficult. You can solve by square roots. Remember, you cannot take the square root of a negative number. However, there are 2 answers to a square root: the positive and negative root.

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Vocabulary Perfect Square Perfect Square: A number whose square roots are integers. Square Root Square Root: one of the equal factors that makes up the square. – Uses the “√ ” symbol – Has a positive and negative solution Principle Square Root Principle Square Root: the positive square root

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Squares & Square Roots Squares and square roots are inverse operations because they are opposites.

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Finding Squares List the squares up to 30. 1 2 =11 2 =21 2 = 2 2 =12 2 =22 2 = 3 2 =13 2 =23 2 = 4 2 =14 2 =24 2 = 5 2 =15 2 =25 2 = 6 2 =16 2 =26 2 = 7 2 =17 2 =27 2 = 8 2 =18 2 =28 2 = 9 2 =19 2 =29 2 = 10 2 =20 2 =30 2 =

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Finding Squares List the squares up to 30. 1 2 =111 2 =12121 2 =441 2 2 =412 2 =14422 2 =484 3 2 =913 2 =16923 2 =529 4 2 =1614 2 =19624 2 =576 5 2 =2515 2 =22525 2 =625 6 2 =3616 2 =25626 2 =676 7 2 =4917 2 =28927 2 =729 8 2 =6418 2 =32428 2 =784 9 2 =8119 2 =36129 2 =841 10 2 =10020 2 =40030 2 =900

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Solving by Square Roots To solve by square root: 1)Quadratic does NOT have a b. Only ax 2 + c = 0 2)Isolate the variable by inverse operations. 3)Square root both sides, if possible. 4)Write solution as + and – answer.

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Practice

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Simplify, then Root 1)Isolate x 2 2)Take the square root of both sides

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Practice

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Approximating Solutions When factoring doesn’t work, and it isn’t a perfect square, then you must round your answer.

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Summary Answer the essential question in detailed, complete sentences. How do you solve a quadratic equation by graphing and square roots? Write 3-5 study questions in the left column to correspond with the notes.

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