1. Warm-up:
Solve: 2x2 + 4x – 5 = 0
HW : pg (25, 27, 31, 43, 46, 47, 64, 67, 76, 93, 96, 100, , 107, 108,117, 119)

2. HW Answers: pg (16,18, 20, 24, 26, 28, 30, 44, 45, 49, 52, 54, 59, 60, 62, 68, 69, 72, 74, 79)
16) 3
18) -10
20) 50
24) ½
26) 0
28) 9/7
30) 7/4
44) ± 1 3
45) 4, -2
49) − 3 2 , 11
52) 0, ± 5 2
54) 3, 1, -1
59) ±2 3 ; ±3.46
60) ± 5 3 ; ±1.67
62) −13± 21 ;−8.42, −17.58
68) −4± 2
69) 2±2 3
72) 1, -1/2
74) 1 2 ±
79) 2/7

3. Objective: Check/Find solutions by calculator.
Solve polynomial equations of a higher degree
Solve radical and rational exponent equations.
Solve absolute value equations.

4. Check/Find Solutions by calculator:
Check?Find the zeros by graphing the related quadratic function,
using the ZERO function of a graphing calculator.
Type equation using [y=] then hit [graph]. Be sure to use an appropriate window!
Press [2nd] [CALC] [2]
Left Bound?  a number to left of the zero such as -5
Right Bound?  a number to the right of the zero such as -1
Guess? a value close to the zero on the graph such as -3
the approximate zeros of the related function are –2.9 and 0.9.
Example 5-3a

5. Solving Polynomial Equations of Higher Degree:
set equal to zero and factor
3x4 = 48x2
Careful!
Do not simplify by dividing each side by x2.
The solution 0 will be lost.
3x4 – 48x2 = 0
Set equal to zero.
3x2(x2 – 16) = 0
Factor.
3x2(x + 4)(x – 4) = 0
ZPP
3x2 = 0
x – 4 = 0
x + 4 = 0
x = 0
x = 4
x = – 4
Check for extraneous solutions!

6. Solving a radical equation containing one square root:
1. Isolate the radical on one side of the equation.
2. Square both sides of the equation.
3. Solve for the variable.
4. Check the solutions.
Example: Solve
Isolate the radical.
Square both sides.
Solve for x.
Check.

7. Example: Solve
Isolate the radical.
Square both sides.
Solve for x.
Check your Solutions!

8. Solve: Check your solution! Isolate the rational exponent
Raise both sides to the reciprocal power
Take the fourth root of 16 then raise to the third power
Check your solution!

9. Can graphing calculators help?
SURE!
[y=] Input for Y1
and x-2 for Y2
[Graph] (make sure
window is appropriate)
Find the points of
intersection
[2nd] [calc] [5] [enter] [enter] [enter]
One Solution at x = 4
Check to see if the solution is extraneous!

10. Absolute Value Equations
Isolate the absolute value.
Apply Absolute Value Rule
Check your Solutions!

11. Summary: Check/Find solutions by calculator.
Solve polynomial equations of a higher degree
Solve radical and rational exponent equations.
Solve absolute value equations.

12. Sneedlegrit: Solve: 2𝑥+7 −𝑥=2
HW : pg (25, 27, 31, 43, 46, 47, 64, 67, , 93, 96, 100, 102, 107, ,117, 119)