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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 ab = a ∙ b EXAMPLE: 20 = 4 ∙ 5 = 4 ∙ 5=2 5 Chapter 9 Test Review Simplify the expression. Chapter 9 Test Review Simplify the expression. Chapter 9 Test Review Simplify the expression. 36 24 Chapter 9 Test Review Simplify the expression. 8 6 9.5 Solving Quadratic Equations by Graphing The x-intercepts of graph y = 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 QUADRATIC FORMULA The solutions of the quadratic equation ax2 + bx + c = 0 are: x= − ± 2 −4 2 when a ≠ 0 and b2 – 4ac > 0. 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= − ± 2 −4 2 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