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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 a square root of 9.
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.
Chapter 9 Test Review
Evaluate the expression.
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Chapter 9 Test Review
Evaluate the expression.
Chapter 9 Test Review
Evaluate the expression.
Chapter 9 Test Review
Evaluate the expression.
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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.
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
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
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.
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
In the quadratic formula, the expression inside the radical is the DISCRIMINANT.
x =
9.7 Using the Discriminant
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
