Ch. 9 & 10

Question 1

polynomial

Answer 1

an expression that can be written as a monomial/sum of monomials w/ whole # exponents

Question 2

degree

Answer 2

(of a polynomial) the largest exponent

Question 3

what can a polynomial NOT be?

Answer 3

it can’t have negative or fractional exponents it can’t have variables in denominators

Question 4

polynomial equation

Answer 4

an equation that can be written w/ a polynomial as 1 side & 0 as the other side

Question 5

standard form

Answer 5

(of polynomials) from left to right, exponents go from largest to smallest

Question 6

rational number

Answer 6

can be written as quotient of 2 integers

Question 7

rational expression

Answer 7

an expression that can be written as the quotient of 2 polynomials

Question 8

rational equation

Answer 8

an equation with only rational expressions on both sides

Question 9

Product of Powers Rule

Answer 9

a^m • aⁿ = a^{m + n}

Question 10

Quotient of Powers Rule

Answer 10

a^m/aⁿ = a^{m - n}

a does not equal 0

Question 11

how to factor polynomials

Answer 11

1. facor out any GCF’s
2. factor normally (ax² + bx + c)

Question 12

ratio of the volume of two spheres

Answer 12

is equal to the ratio of the cubes of their diameters

Question 13

Power of a Power Rule

Answer 13

(a^m)ⁿ = a^mn

Question 14

Power of Product Rule

Answer 14

(ab)ⁿ = aⁿbⁿ

Question 15

Power of a Quotient Rule

Answer 15

(a/b)ⁿ = aⁿ/bⁿ

b does not equal 0

Question 16

how to solve rational equations

Answer 16

1. find LCD of all 3 & make the denominators all the same and cancel them out OR find LCD of left side denominators, make them the same, and then cross multiply
2. simplify

Question 17

extraneous solution

Answer 17

when a solution is not a solution of the original equation

(test it)

Question 18

point of no return

Answer 18

the point where it would take as much time to return to the starting point as to continue on to the destination.

use t = d/r

d/r = d/r

Question 19

cubic function

Answer 19

a polynomial function of degree 3

Question 20

zero of a function

Answer 20

value of x that makes y = 0, same as x-intercept

Question 21

double zero

Answer 21

cubic function w/ a squared factor

Question 22

triple zero

Answer 22

a cubic function w/ a cubed factor

Question 23

y = (x - 2)³

Answer 23

intersects x-axis once

Question 24

y = (x - 2)²(x + 1)

Answer 24

intersects x-axis twice

Question 25

y = (x - 2)(x + 1)(x + 4)

Answer 25

intersects x-axis three times

Question 26

steps to solve a cubic equation w/out graphing

Answer 26

1. put y on left side and set it to 0
2. find the GCF of the right side if possible and factor it out
3. if ax² + bx + c format, use quadratic formula

Question 27

how to solve cubic equations w/ calculator

Answer 27

1. input equation
2. find x-intercept (where y = 0)

Question 28

square root of negative number

Answer 28

becomes i • pos. square root

Question 29

parametric equation

Answer 29

equations where two variables are expressed in terms of a 3rd variable

Question 30

parameter

Answer 30

3rd variable of a parametric equation

Question 31

how to graph a parametric equation

Answer 31

1. make a table of values (time, x, y)
2. graph using x & y

OR

1. change to PAR mode
2. input equations

Question 32

how to write an equation for y interms of x

Answer 32

1. solve for t with either of the equations (preferably x)
2. substitute into the other equation not used in step 1, t
3. simplify

Question 33

3D coordinate plane

Answer 33

Question 34

how to find a coordinate on a coordinate plane

Answer 34

Question 35

3D midpoint formula

Answer 35

(x₁ + x₂/2, y₁ + y₂/2, z₁ + z₂/2)

Question 36

length of a diagonal of a rectangular prism

Answer 36

with edges of length x, y, and z & a diagonal of length d

d = square root of x₂ + y₂ + z₂

Question 37

3D distance formula

Answer 37

d = square root of (x₂ - x₁)2 + (y₂ - y₁)2 + (z₂ - z₁)2

Question 38

equatons of circles and spheres centered at the origin

Answer 38

circle ⇒ x² + y² = r²

Question 39

how to graph circle x² + y² = 36

Answer 39

1. since it’s this form, center is (0,0) and r² = 36; r = 6; sketch circle with center at Origin and (0,6) at top, (6,0) at right, (0, -6) at bottom, and (-6,0) at left
2. use a graphing calculator; graph two semicricles ⇒ x² + y² = 36 ⇒ y² = 36 - x²⇒ y = pos/neg square root of 36 - x² to make circle circular, use Zoom Square

Question 40

how to find the equation of a circle/sphere

Answer 40

1. find center
2. decide if it is at O or other and use the right equation
3. find length of radius
4. plug in radius

Question 41

equations of circles not centered at origin

Answer 41

center (h,k) radius r

(x - h)² + (y - k)² = r²