9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 =...
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Transcript of 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 =...
![Page 1: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/1.jpg)
9.1 Square Roots
SQUARE ROOT OF A NUMBERIf 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.
![Page 2: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/2.jpg)
Chapter 9 Test Review
Evaluate the expression.
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![Page 3: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/3.jpg)
Chapter 9 Test Review
Evaluate the expression.
![Page 4: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/4.jpg)
Chapter 9 Test Review
Evaluate the expression.
![Page 5: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/5.jpg)
Chapter 9 Test Review
Evaluate the expression.
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![Page 6: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/6.jpg)
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.
![Page 7: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/7.jpg)
Chapter 9 Test Review
Solve the equation.
x2 = 144
![Page 8: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/8.jpg)
Chapter 9 Test Review
Solve the equation.
8x2 = 968
![Page 9: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/9.jpg)
Chapter 9 Test Review
Solve the equation.
5x2 – 80 = 0
![Page 10: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/10.jpg)
Chapter 9 Test Review
Solve the equation.
3x2 – 4 = 8
![Page 11: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/11.jpg)
9.3 Simplifying Radicals
PRODUCT PROPERTY OF RADICALS =
EXAMPLE: = = = 2
![Page 12: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/12.jpg)
Chapter 9 Test Review
Simplify the expression.
![Page 13: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/13.jpg)
Chapter 9 Test Review
Simplify the expression.
![Page 14: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/14.jpg)
Chapter 9 Test Review
Simplify the expression.
![Page 15: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/15.jpg)
Chapter 9 Test Review
Simplify the expression.
![Page 16: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/16.jpg)
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.
9.5 Solving Quadratic Equations by Graphing
![Page 17: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/17.jpg)
Chapter 9 Test Review
Use a graph to estimate the solutions of the equation. Check your solutions
algebraically.x2 – 3x = -2
![Page 18: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/18.jpg)
Chapter 9 Test Review
Use a graph to estimate the solutions of the equation. Check your solutions
algebraically.-x2 + 6x = 5
![Page 19: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/19.jpg)
Chapter 9 Test Review
Use a graph to estimate the solutions of the equation. Check your solutions
algebraically.x2 – 2x = 3
![Page 20: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/20.jpg)
THE QUADRATIC FORMULA
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.
![Page 21: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/21.jpg)
Chapter 9 Test Review
Use the quadratic formula to solve the equation.
3x2 – 4x + 1 = 0
![Page 22: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/22.jpg)
Chapter 9 Test Review
Use the quadratic formula to solve the equation.
-2x2 + x + 6 = 0
![Page 23: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/23.jpg)
Chapter 9 Test Review
Use the quadratic formula to solve the equation.
10x2 – 11x + 3 = 0
![Page 24: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/24.jpg)
In the quadratic formula, the expression inside the radical is the DISCRIMINANT.
x =
9.7 Using the Discriminant
DISCRIMINANT- 4ac
![Page 25: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/25.jpg)
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
![Page 26: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/26.jpg)
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
![Page 27: 9.1 Square Roots SQUARE ROOT OF A NUMBER If b 2 = a, then b is a square root of a. Examples: 3 2 = 9, so 3 is a square root of 9. (-3) 2 = 9, so -3 is.](https://reader035.fdocuments.us/reader035/viewer/2022062407/56649d875503460f94a6c698/html5/thumbnails/27.jpg)
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