User's Manual
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
0GD2T3U1EÕ 2187
(ab)
r
= a
r
b
r
(3 x 2)
4
= 3
4
x 2
4
0 G 1 V / G 1 Õ1296
= (b
≠
0) = 0 G 1 W / G 1 Õ 5.0625
a =
√
a
r
9=
√
9
2
1 ç 2 D 6 G / E Õ3
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/V0EÕ 0.869
2(3)
-9.211 M68/..WD/V0EÕ -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
- 4ac
2a
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
´´ µµ JJ
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