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.
- 𝟒
Chapter 9 Test Review
Evaluate the expression.
𝟏𝟒𝟒
Chapter 9 Test Review
Evaluate the expression.
𝟏𝟎𝟎
Chapter 9 Test Review
Evaluate the expression.
- 𝟐𝟓
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.
𝟒𝟓
Chapter 9 Test Review
Simplify the expression.
𝟐𝟖
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=
−𝑏 ± 𝑏 2 −4𝑎𝑐
2𝑎
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=
−𝑏 ± 𝑏2 −4𝑎𝑐
2𝑎
DISCRIMINANT
𝐛𝟐 - 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