Liner and quadratic functions

Question 1

What do linear functions look like when graphed

Answer 1

Straight lines

Question 2

Is is the regular form for linear functions

Answer 2

ax+b=0

Question 3

Is is the regular form for quadratic functions

Answer 3

ax^2+bx+c=0 & a=/=0

Question 4

What are the solutions to the quadratic functions form of x^2 - p=0

Answer 4

x = sqrt(p) & -sqrt(p)

Question 5

When does x^2 - p = 0 have two real solutions

Answer 5

when p > 0

Question 6

When does x^2 - p = 0 have one real solution

Answer 6

when p = 0

Question 7

When does x^2 - p = 0 have no real solutions

Answer 7

when p < 0

Question 8

What are the solutions to the quadratic functions form of k * (x - r) ^ 2 - p = 0

Answer 8

x = r + sqrt(p/k) & r - sqrt(p/k)

Question 9

What can the value of k not be in k * (x - r) ^ 2 - p = 0

Answer 9

0

Question 10

When does k * (x - r) ^ 2 - p = 0 have two real solutions

Answer 10

when p/k>0

Question 11

When does k * (x - r) ^ 2 - p = 0 have two real solutions

Answer 11

when p=0

Question 12

When does k * (x - r) ^ 2 - p = 0 have two real solutions

Answer 12

when p/k<0

Question 13

For the form ax^2 + bx + c what is the discriminit

Answer 13

b^2-4ac

Question 14

What can a discriminant of a quadratic equation tell us

Answer 14

How many solutions there are

Question 15

if the discriminant of a quadratic is above 0, how many real solutions are there

Answer 15

2

Question 16

if the discriminant of a quadratic is equal to 0, how many real solutions are there

Answer 16

1

Question 17

if the discriminant of a quadratic is below 0, how many real solutions are there

Answer 17

0

Question 18

What is the quadratic formula

Answer 18

x = (- b +/- sqrt(b^2-4ac))/2a

Question 19

In the form ax^2+bx+c for a quadratic formula what can a not be

Answer 19

0

Question 20

What is the standard form for a polynomial

Answer 20

ax^n+bx^(n-1)+cx^(n-2)……+dx^2+ex+f where n is a non negative integer

Question 21

for the standard form for a polynomial what can a not be

Answer 21

0

Question 22

When are two polynomials equal

Answer 22

when they have the same coefficients of each term

Question 23

How do we add polynomials

Answer 23

we add each of the coefficients for each individual terms. Ex. 7x^2-8x+4 + 8x^2+9x-2 = (7+0)x^3+(8+0)x^2+(9+(-8))x+(4-2) = 7x^3+8x^2+x+2

Question 24

How do we subtract polynomials

Answer 24

we add each of the coefficients for each individual terms. Ex. 7x^2-8x+4 + 8x^2+9x-2 = (7-0)x^3+(0-8)x^2+((-8)-9)x+(4-(-2)) = 7x^308x^2-17x+6

Question 25

How do we multiply polynomials

Answer 25

we add all the coefficients of product of the terms who powers add to each integers power Ex. (2x^2+4x+5) * (3x^2-5x-2) = (2*3)x^4+(4*3+2*(-5))x^3+(2*(-2)+4*(-5)+(5*3))x^2+(4*2+(-5)*5)x+(-2)*5 = 6x^4+2x^3-9x^2-21x-10

Question 26

What is the prime factorization of a number

Answer 26

the factors of the number in such a way where all the factors are prime. Ex 324 = 3^4 * 2^2

Question 27

what would we get If we divide two numbers where the denominator has a prime factor that the numerator does not Ex. 12/5

Answer 27

You get a rational number or remainder

Question 28

what would we get If we divide two numbers where every prime factor in the denominator is also in the numerator Ex. 12/6

Answer 28

a integer or a number with no remaineder

Question 29

What is the division algorithm for polynomials

Answer 29

for any non zero polynomial P(x) and K(x) there exists Q(x) & R(x) such that P(x)=Q(x)K(x)+R(x) so P(x)/K(x)=Q(x) with a remainder of R(x)

Question 30

When do you get no remainder for a quotient of polynomial

Answer 30

when the factors of the denominator are all in the numorator

Question 31

What is the rational root theorem

Answer 31

If P(x)=ax^n+bx^(n-1)+....cx^2+dx+e, P(m/n)=0,& m shares no factors with n, then a/m & e/n are both integers

Question 32

If R is the remainder of a polynomial P(x) divided by x-a then what is R

Answer 32

R=P(a)

Question 33

If (a polynomial) P(x) is divisible by x-a then what is P(a)

Answer 33

P(a)=0

Question 34

If P(a)=0 then what is the remainder of P(x)/(x-a) (P(x) is a polynomial)

Answer 34

0