Algebra

FUNCTIONS

100

what is the domain?

x-values,input,independent value

200

f(x)=5x+1

when x equals 3

f(x)=16 or 16=f(x)

300

f(x)=2x²+8x+2

average rate of change over the interval .5 and 2

-2

400

f(x)=16x²+12x+2

over the interval [0.25,0.5]

8

500

2x²+4x+3

find axis of symmetry,vertex,y-intercept

y-intercept=3

axis of symmetry=-1

vertex=(-1,1)

POLYNOMIALS

100

what is a term?

everything separated by + and -

200

7x-5-x³+6x⁴-3x²

put in standard form

6x⁴-x³-3x²+7x-5

300

-4x³(x²+3x-4)

-4x⁵-12x⁴+16x³

400

(6x²+3x-2)(3x²+5x-8)

3x²-2x+6

500

(x²+2x+3)+(4x²+5)

5x²+2x+8

QUADRATIC EQUATIONS

100

x²+9x=-20

x=-4 and x=-5

200

x²+16x+64=0

x=-8 and x=-8

500

f(x)=x²-2x=8

x intercepts for parabola

find vertex

x intercepts= -2 and 4

vertex=(1,-9)

FACTORING

100

x²+3x-40

(x-5) (x+8) 

200

Factor

x²+9x=-20

x=-4 or x=-5

300

12x⁵+8x⁴-6x⁵

2x³

400

x²+10xy+24y²

(x+6y) (x+4y)

500

3x³+15x²-18x

3x(x-1)(x+6)

ABSOLUTE VALUE

100

7=|x|+2

|x|=-5 and |x|=5

200

6=|x|-2

|x|=8 and |x|=-8

300

|2x-3|=1

x=2 

x=1

400

|3x-6|=12

x=6

x=-6

500

3|x+6|+8=5

|x+6|=-1

no solution, the distance from zero can't be negative