Texas Instruments Algebra with the TI-84 Plus Silver Edition, Law of Exponents & Radicals

Algebra with the TI-84 Plus Silver Edition

Law of Exponents & Radicals

Formulas	Examples	Keystrokes
	(where a=3, b=2, P=5,
	Q=6, r=4, s=2)

Graphing Inequalities

ar x a s = a r + s

ar

as = ar – s

ap aq

34 x 3 2 = 3 4 + 2	0GD1T/E Õ729
34
32 = 34 – 2	0GD1U/E Õ9
35 x 36

The Inequality GraphingApp for The intersection ofy ≤ 2x-3

ar

= ap + q – r

34 = 35 + 6 – 4 0GD2T3U1EÕ2187

the TI-84 Plus Silver Edition is	and y > .5x2-7is shaded.
used here to enter the equations

(ab)r = arbr

(a ) r = ar (b ≠ 0)

b br

a r = s√ar

s

a0 = 1 (a ≠ 0)

a–r= 1 (a ≠ 0) ar

(3 x 2)4 = 34 x 24						0G1V/G1	Õ1296
3		4			34
(		)	=				Õ5.0625
	2				24	0G1W/G1
2			4			1 ç2D6G/E Õ3
9 4 =			√92
30 = 1						0G7 Õ1
3-4 =				1		.W0G1 Õ.0123

34

y ≤ 2x-3 and y > .5x2-7.

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.

1Enter equations in the oeditor.

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 2b + 3ab 2 + b 3 (a – b) 3 = a 3 – 3a 2b + 3ab 2 – b 3

(a + b) 4 = a 4 + 4a 3b + 6a 2b2 + 4ab 3 + b 4

(a + b) 5 = a 5 + 5a 4b + 10a 3b2 + 10a 2b3 + 5ab 4 + b 5

Factoring

a2 – b 2 = (a + b) (a – b)

a2 + 2ab + b 2 = (a + b) 2 a2 – 2ab + b 2 = (a – b) 2

a3 + b 3 = (a + b) (a 2 – ab + b 2) a3b – ab = ab (a + 1) (a – 1)

a3 – 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! = ￿ç4 Õ120

Logarithms ´µJ

y = log				x means ay = x		log xr = r log x		log x = log			x
		a				a	a		10
loga xy = loga x + loga y						loga 1 = 0				log10 x
log	x		= log		x – log y	log	a = 1	log x =
a y				a	a	a		a	log		a
In x = loge x						ln e = 1			10

2Press sto graph both equations.

(You may need to adjust the viewing window.)

3Press y/5: intersect to find the point of intersection.

4Press Õto 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 x = –b± √b2 - 4ac

								2a
Example: 3x2 + 2x - 4								(where a=3, b=2, c=-4)
		-2± √
	x =					2 2	- 4(3)(-4)
			2(3)					Keystrokes
Step 1	22 - 4(3)(-4)							/FU1V0VM1 Õ52
Step 2	-2 +		√					M/T%b2/E Õ5.211
					52
	-2 -	√						M/U%b2/E Õ-9.211
				52
Step 3	5.211							28/..WD/V0EÕ0.869
	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 polynomialx2 - 5x + 6.

1Press ç0: Solver…

2Enter equation (must be in form where equation is set equal to 0) and press Õ.

3Place cursor next to variable for which you would like to solve.

4Enter a guess for the value.

5 Press É\to see a solution.

© Texas Instruments, 2007 education.ti.com