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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Presentation transcript:

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

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

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

Solving by Graphing

Practice 1) x = 02) -½ x = 0

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.

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

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

Finding Squares List the squares up to =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 =

Finding Squares List the squares up to =111 2 = = =412 2 = = =913 2 = = = = = = = = = = = = = = = = = = = = = = =900

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.

Practice

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

Practice

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

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.