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Quadratic Equations and Functions

Quadratic Equations and Functions . 9.1 Solving Quadratic Equations by Finding Square Roots . 9.1 Objectives . Goal 1: Evaluate and approximate square roots. Goal 2: Solve a quadratic equation by finding square roots. . Square Root of a Number . If = a, then b is a square root of a.

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Quadratic Equations and Functions

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  1. Quadratic Equations and Functions 9.1 Solving Quadratic Equations by Finding Square Roots

  2. 9.1 Objectives • Goal 1: Evaluate and approximate square roots. • Goal 2: Solve a quadratic equation by finding square roots.

  3. Square Root of a Number • If = a, then b is a square root of a. • Example: If = 9, then 3 is a square root of 9.

  4. Vocabulary • Is the number or expression inside a radical symbol . • Are numbers whose square roots are integers or quotients of integers. • Radicand • Perfect Squares

  5. Vocabulary • The square roots of numbers that are not perfect squares. • Is an equation that can be written in the standard from of a + bx + c = 0, where a ≠ 0. In standard form a is the leading coefficient. • Irrational Numbers • Quadratic Equation

  6. Finding Square Roots of a Number • a.) = • b.) - = • c.) = • d.) ± = • e.) = 8, Positive square root -8, Negative square root 0, Square root of zero ± 0.5 Two square roots Undefined (No real square roots) All positive real numbers have two square roots: a positive square root and a negative square root.

  7. Perfect Squares and Irrational Numbers • a.) - = • b.) = • c.) = • d.) = • e.) =

  8. Perfect Squares and Irrational Numbers • a.) - = -11, 121 is a perfect square: = 121 • b.) = -1.2, 1.44 is a perfect square: = 1.44 • c.) = 0.3, 0.09 is a perfect square: = 0.09 • d.) ≈ 2.65, 7 is not a perfect square; it is irrational • e.) ≈3.61,13 is not a perfect square; it is irrational The square roots of numbers that are not perfect squares must be written using the radical symbol or approximated ≈.

  9. Evaluating a Radical Expression • Evaluate when a = 1, b = -2, and c = -3 • = = = = 4 Positive Square Root

  10. Evaluating a Radical Expression • Evaluate when a = 4, b = 5, and c = 1

  11. Evaluating a Radical Expression • Evaluate when a = 3, b = -7, and c = 6

  12. Solving a Quadratic Equation in the form of = d by finding square roots • If d > 0, • If d = 0, • If d < 0, • Then = d has two solutions: x = ± . • Then = d has one solution: x = 0. • Then = d has no real solutions.

  13. Solving Quadratics • a.) = 4 • b.) = 5 • c.) = 0 • d.) = -1

  14. Solving Quadratics • a.) = 4: has two solutions x = +2, x = -2. • b.) = 5: has two solutions x = , x = -. • c.) = 0: has one solution: x = 0. • d.) = -1: has no real solution.

  15. Rewriting Before Solving Square Roots • Solve 3 - 48 = 0 • 3= 48 • = 16 • x = ± • x = ± 4 • Steps: • Add 48 to each side. • Divide each side by 3. • Find square roots. • 16 is a perfect square: = 16 and = 16 The solutions are 4 and -4. Check your answer.

  16. Rewriting Before Solving Square Roots • Solve + 3 = 12

  17. Rewriting Before Solving Square Roots • Solve - 12 = 0

  18. Rewriting Before Solving Square Roots • Solve + 12 = 5

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