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Understanding Square Roots and Solving Quadratic Equations

This comprehensive guide covers the concept of square roots, including definitions, examples, and the fundamental properties of square roots. It explores methods for solving quadratic equations, including isolating terms, graphing techniques, using the quadratic formula, and understanding discriminants. Detailed examples illustrate each method, ensuring a clear understanding of these key algebraic concepts. Whether you're simplifying radicals or solving equations, this resource is designed to enhance your math skills effectively.

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Understanding Square Roots and Solving Quadratic Equations

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  1. 9.1 Square Roots SQUARE ROOT OF A NUMBER If b2 = a, then b is a square root of a. Examples:32= 9, so 3 is a square root of 9. (-3)2= 9, so -3 is a square root of 9.

  2. Chapter 9 Test Review Evaluate the expression. -

  3. Chapter 9 Test Review Evaluate the expression.

  4. Chapter 9 Test Review Evaluate the expression.

  5. Chapter 9 Test Review Evaluate the expression. -

  6. 9.2 Solving Quadratic Equations by Finding Square Roots QUADRATIC EQUATION When b = 0, this equation becomes ax2 + c = 0. One way to solve a quadratic equation of the form ax2+ c = 0 is to isolate the x2 on one side of the equation. Then find the square root(s) of each side.

  7. Chapter 9 Test Review Solve the equation. x2 = 144

  8. Chapter 9 Test Review Solve the equation. 8x2= 968

  9. Chapter 9 Test Review Solve the equation. 5x2 – 80 = 0

  10. Chapter 9 Test Review Solve the equation. 3x2 – 4 = 8

  11. 9.3 Simplifying Radicals PRODUCT PROPERTY OF RADICALS = EXAMPLE: = = = 2

  12. Chapter 9 Test Review Simplify the expression.

  13. Chapter 9 Test Review Simplify the expression.

  14. Chapter 9 Test Review Simplify the expression.

  15. Chapter 9 Test Review Simplify the expression.

  16. 9.5 Solving Quadratic Equations by Graphing The x-intercepts of graphy = ax2 + bx + c are the solutions of the related equations ax2 + bx + c = 0. Recall that an x-intercept is the x-coordinate of a point where a graph crosses the x-axis. At this point, y = 0.

  17. Chapter 9 Test Review Use a graph to estimate the solutions of the equation. Check your solutions algebraically. x2 – 3x = -2

  18. Chapter 9 Test Review Use a graph to estimate the solutions of the equation. Check your solutions algebraically. -x2 + 6x = 5

  19. Chapter 9 Test Review Use a graph to estimate the solutions of the equation. Check your solutions algebraically. x2 – 2x = 3

  20. 9.6 Solving Quadratic Equations by the Quadratic Formula The solutions of the quadratic equation ax2 + bx + c = 0 are: x = when a ≠ 0 and b2 – 4ac > 0. THE QUADRATIC FORMULA

  21. Chapter 9 Test Review Use the quadratic formula to solve the equation. 3x2 – 4x + 1 = 0

  22. Chapter 9 Test Review Use the quadratic formula to solve the equation. -2x2 + x + 6 = 0

  23. Chapter 9 Test Review Use the quadratic formula to solve the equation. 10x2– 11x + 3 = 0

  24. 9.7 Using the Discriminant In the quadratic formula, the expression inside the radical is the DISCRIMINANT. x = DISCRIMINANT - 4ac

  25. Chapter 9 Test Review Find the value of the discriminant. Then determine whether the equation has two solutions, one solution, or no real solution. 3x2 – 12x + 12 =0

  26. Chapter 9 Test Review Find the value of the discriminant. Then determine whether the equation has two solutions, one solution, or no real solution. 2x2 + 10x + 6=0

  27. Chapter 9 Test Review Find the value of the discriminant. Then determine whether the equation has two solutions, one solution, or no real solution. -x2 + 3x - 5 =0

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