Law of Exponents & Radicals
Formulas
Examples
Keystrokes
(where a=3, b=2, P=5,
Q=6, r=4, s=2)
a
r
x a
s
= a
r + s
3
4
x 3
2
= 3
4 + 2
0 G D 1 T / E
Õ
729
= a
r – s
= 3
4 – 2
0 G D 1 U / E
Õ
9
= a
p + q – r
= 3
5 + 6 – 4
0GD2T3U1E
Õ
2187
(ab)
r
= a
r
b
r
(3 x 2)
4
= 3
4
x 2
4
0 G 1 V / G 1
Õ
1296
= (b
≠
0)
=
0 G 1 W / G 1
Õ
5.0625
a
=
√
a
r
9
=
√
9
2
1
ç
2 D 6 G / E
Õ
3
a
0
= 1 (a
≠
0)
3
0
= 1
0 G 7
Õ
1
a
–r
= (a
≠
0)
3
-4
=
. W 0 G 1
Õ
.0123
a
r
a
s
3
4
3
2
a
b
a
r
b
r
( )
a
p
a
q
a
r
r
3
2
3
4
2
4
( )
4
r
s
s
3
5 x
3
6
3
4
2
4
4
Graphing Inequalities
Solving Linear Systems by Graphing
The intersection of two functions is the solution to the system.
Graphing provides a quick and powerful way to solve linear systems.
1
Enter equations in the
o
editor.
2
Press
s
to graph both equations.
(You may need to adjust the viewing window.)
3
Press
y /
5: intersect
to find the point of intersection.
4
Press
Õ
to select the 1st curve and again to select the 2nd curve.
5
Enter your best guess and press
Õ
.
Quadratic Formula
If
a
≠
0
, the roots of
ax
2
+ bx + c = 0
are
Example:
3x
2
+ 2x - 4
(where a=3, b=2, c=-4)
Keystrokes
Step 1
2
2
- 4(3)(-4)
/ F U 1 V 0 V M 1
Õ
52
Step 2
-2 +
√
52
M / T % b 2 / E
Õ
5.211
-2 -
√
52
M / U % b 2 / E
Õ
-9.211
Step 3
5.211
28/..WD/V0E
Õ
0.869
2(3)
-9.211
M68/..WD/V0E
Õ
-1.535
2(3)
Using the Equation Solver
Use the Equation Solver on your TI-84 Plus Silver Edition to solve for any
variable in an equation. In this example, the Solver is being used to find
one of the roots of the polynomial
x
2
- 5x + 6
.
1
Press
ç
0: Solver…
2
Enter equation (must be in form where equation is set equal to 0)
and press
Õ
.
3
Place cursor next to variable for which you would like to solve.
4
Enter a guess for the value.
5
Press
É \
to see a solution.
x
=
–
b
±
√
b
2
- 4
ac
2
a
Binomial Expansion
a (b + c) = ab + ac
(a + b) (c + d) = ac + ad + bc + bd
(a + b)
2
= a
2
+ 2ab + b
2
(a – b)
2
= a
2
– 2ab + b
2
(a + b)
3
= a
3
+ 3a
2
b + 3ab
2
+ b
3
(a – b)
3
= a
3
– 3a
2
b + 3ab
2
– b
3
(a + b)
4
= a
4
+ 4a
3
b + 6a
2
b
2
+ 4ab
3
+ b
4
(a + b)
5
= a
5
+ 5a
4
b + 10a
3
b
2
+ 10a
2
b
3
+ 5ab
4
+ b
5
Factoring
a
2
– b
2
= (a + b) (a – b)
a
2
+ 2ab + b
2
= (a + b)
2
a
2
– 2ab + b
2
= (a – b)
2
a
3
+ b
3
= (a + b) (a
2
– ab + b
2
)
a
3
b – ab = ab (a + 1) (a – 1)
a
3
– b
3
= (a – b) (a
2
+ ab + b
2
)
Factorial
n! = n (n-1) (n-2) ... (2) (1)
Example:
5!
= 5 (4) (3) (2) (1)
Keystrokes:
5! =
ç |
4
Õ
120
Logarithms
´
´ µ
µ J
J
y = log
a
x means a
y
= x
log
a
x
r
= r log
a
x
log x = log
10
x
log
a
xy = log
a
x + log
a
y
log
a
1 = 0
log
a
= log
a
x – log
a
y
log
a
a = 1
log
a
x =
log
10
x
In x = log
e
x
ln e = 1
x
= -
2
±
√
2
2
-
4(3)(-4)
2(3)
education.ti.com
© Texas Instruments, 2007
Algebra with the TI-84 Plus Silver Edition
1
a
r
x
y
1
3
4
The
Inequality Graphing
App for
the TI-84 Plus Silver Edition is
used here to enter the equations
y
≤
2x-3
and
y > .5x
2
-7
.
The intersection of
y
≤
2x-3
and
y > .5x
2
-7
is shaded.
log
10
a
