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## 9.1 Square Roots

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**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.**Chapter 9 Test Review**Evaluate the expression. -**Chapter 9 Test Review**Evaluate the expression.**Chapter 9 Test Review**Evaluate the expression.**Chapter 9 Test Review**Evaluate the expression. -**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.**Chapter 9 Test Review**Solve the equation. x2 = 144**Chapter 9 Test Review**Solve the equation. 8x2= 968**Chapter 9 Test Review**Solve the equation. 5x2 – 80 = 0**Chapter 9 Test Review**Solve the equation. 3x2 – 4 = 8**9.3 Simplifying Radicals**PRODUCT PROPERTY OF RADICALS = EXAMPLE: = = = 2**Chapter 9 Test Review**Simplify the expression.**Chapter 9 Test Review**Simplify the expression.**Chapter 9 Test Review**Simplify the expression.**Chapter 9 Test Review**Simplify the expression.**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.**Chapter 9 Test Review**Use a graph to estimate the solutions of the equation. Check your solutions algebraically. x2 – 3x = -2**Chapter 9 Test Review**Use a graph to estimate the solutions of the equation. Check your solutions algebraically. -x2 + 6x = 5**Chapter 9 Test Review**Use a graph to estimate the solutions of the equation. Check your solutions algebraically. x2 – 2x = 3**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**Chapter 9 Test Review**Use the quadratic formula to solve the equation. 3x2 – 4x + 1 = 0**Chapter 9 Test Review**Use the quadratic formula to solve the equation. -2x2 + x + 6 = 0**Chapter 9 Test Review**Use the quadratic formula to solve the equation. 10x2– 11x + 3 = 0**9.7 Using the Discriminant**In the quadratic formula, the expression inside the radical is the DISCRIMINANT. x = DISCRIMINANT - 4ac**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**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**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