1. Essential Question: How do we do this stuff?
Chapter 2 Preview
Essential Question: How do we do this stuff?

2. Chapter 2 Preview
Use the x-intercept method to find all real solutions of the equation x3 – 8x2 + 9x + 18 = 0
Graph the function using the graphing calculator
Find the roots
Roots at -1, 3, & 6

3. Chapter 2 Preview Determine the nature of the roots 2x2 – 12x + 18 = 0
Use the discriminant to determine the number of roots:
Discriminant = 0 means “1 real solution”

4. Chapter 2 Preview
Solve by taking the square root of both sides: (4x-4)2 = 25

5. Chapter 2 Preview Solve by factoring: x2 + 2x – 3 = 0
Looking for two numbers that multiply to get -3 and add to get 2
Only ways to multiply to get -3 are
1 • -3 (they add to -2)
-1 • 3 (they add to 2) Hey! We got a winner!
Factor using those numbers
(x – 1)(x + 3) = 0
Set each part of the factorization to 0 to get the solutions
x – 1 = 0 or x + 3 = 0
x = 1 or x = -3

6. Chapter 2 Preview
Solve by using the quadratic formula x2 – 2x – 5 = 0

7. Chapter 2 Preview
Find all solutions: 5x = 2x2 - 1

8. Chapter 2 Preview
Find all solutions: |4 – 0.2x| + 1 = 19

9. Chapter 2 Preview
Find all solutions: |x2 - 10x + 17| = 8

10. Chapter 2 Preview
Find all solutions:

11. Chapter 2 Preview
Find all solutions:

12. Chapter 2 Preview
The problem on the preview has no solution (square roots can’t ever be negative) Find all solutions:

13. Chapter 2 Preview Find all solutions:
Real solutions? When numerator = 0
x2 + 1x – 42 = 0
(x + 7)(x – 6) = 0
x = -7 or x = 6
Extraneous solutions? When denominator = 0
x – 6 = 0
x = 6
When a solution comes up as real and extraneous, the extraneous solution takes precedence
Real solution: x = -7
Extraneous solution: x = 6

14. Chapter 2 Preview Find all solutions:
Real solutions? When numerator = 0
5x2 + 44x + 63 = 0
(5x + 9)(x + 7) = 0
x = -9/5 or x = -7
Extraneous solutions? When denominator = 0
x2 + 12x + 35 = 0
(x + 7)(x + 5) = 0
x = -7 or x = -5
When a solution comes up as real and extraneous, the extraneous solution takes precedence
Real solution: x = -9/5
Extraneous solution: x = -7 or x = -5

15. Chapter 2 Preview Write -4 < x < 9 in interval notation
If an inequality has a line underneath it, we use braces; parenthesis without.
(-4, 9]

16. Chapter 2 Preview
Solve the inequality and express your answer in interval notation: 2x – 6 < 3x + 8
[-14, ∞)

17. Chapter 2 Preview
Solve the inequality and express your answer in interval notation: -15<-3x+3<-3
[2, 6]

18. Chapter 2 Preview
Solve the inequality and express your answer in interval notation:
Critical Points
Real solutions: 5 & -9
Extraneous solution: 1
Test the intervals
(-∞, -9] use x = -10, get -15/11 > 0 FAIL
[-9, 1) use x = 0, get 45 > 0 PASS
(1, 5] use x = 2, get -33 > 0 FAIL
[5, ∞) use x = 6, get 3 > 0 PASS
Interval solutions are [-9, 1) and [5, ∞)

19. Chapter 2 Preview
The simple interest I on an investment of P dollars at an interest rate r for t years is given by I = Prt. Find the time it would take to earn $1800 in interest on an investment of $17,000 at a rate of 6.9%.
You’re given I ($1800), P ($17,000) and r (6.9% = 0.069).
Just plug them into the equation and solve for t
1800 / = (17000)(0.069)(t) / 17000
/ = (0.069)(t) / 0.069
1.53 = t

20. Chapter 2 Preview
d = -16t Find how long it takes the object to reach the ground (d = 0)
Because time is never negative, t = 1.5 s

21. Chapter 2 Preview
128t – 16t2. During what period of time is the arrow above 240 feet

22. Chapter 2 Preview #20, continued Test the intervals
(-∞, 3] -> test x = 0, get 240 < 0 FAIL
[3, 5] -> test x = 4, get -16 < 0 PASS
[5, ∞) -> test x = 6, get 48 < 0 FAIL
The arrow is above 240 ft. from 3 to 5 sec.