Chapter 2 (2.1 to 2.6)

Question 1

What is the standard form of a quadratic and how would you determine its axis of symmetry, y/x intercept(s), vertex, max/min value, and appearance?

Answer 1

f(x) = ax^2 + bx + c
vertex is (-b/2a) for x, plug in for y (axis is x=x-corr)
Y intercept is c, or plug in 0 for x
Plug in 0 for y to find x intercepts
if a>0 it opens up + min if a 1 skinny
|a|

Question 2

What is the vertex form of a quadratic and how would you determine its axis of symmetry, y/x intercept(s), vertex, max/min value, and appearance?

Answer 2

f(x) = a(x - h)^2 + k
Vertex is (h, k)
Plug in 0 for x to find y intercepts  
Plug in 0 for y to find x intercepts
if a>0 it opens up + min if a 1 skinny
|a|

Question 3

What would a function of the first degree look like as an equation, in a graph, and written down?

Answer 3

Y=ax+b

Line starting down, ending up (a>0), starting up, ending down (a

Question 4

What would a function of the second degree look like as an equation, in a graph, and written down?

Answer 4

Y=ax^2+bx+c

Single curve starting up, ending up (a>0), starting down, ending down (a

Question 5

What would a function of the third degree look like as an equation, in a graph, and written down?

Answer 5

Y=ax^3+bx^2+cx+d

Double curve starting down, ending up (a>0), starting up, ending down (a

Question 6

What would a function of the fourth degree look like as an equation, in a graph, and written down?

Answer 6

Y=ax^4+bx^3+cx^2+dx+e

Triple curve starting up, ending up (a>0), starting down, ending down (a

Question 7

What would a function of the fifth degree look like as an equation, in a graph, and written down?

Answer 7

Y=ax^5+bx^4+cx^3+dx^2+ex+f

Four curves starting down, ending up (a>0), starting up, ending down (a

Question 8

How would you divide (x^3-2x^2-9) by (x-3)?

Answer 8

Multiply x-3 to cancel with the first number and add, if it is a factor you will end with 0, if not put the remainder over (x-3)

        x^2+x+3
x-3/x^3-2x^2+0x-9
      x^3-3x^2
               x^2+0x
               x^2-3x
                      3x-9
                      3x-9
                           0

Question 9

How would you synthetically divide (x^3-2x^2-9) by (x-3)?

Answer 9

3] 1 -2 0 -9
3 3 9
1 1 3 0
1x^2=+1x+3

Question 10

How would you synthetically substitute 2 into 2x^6 + 3x^4 - x^2 +3?

Answer 10

2] 2 0 3 0 -1 0 3
4 8 22 44 86 172
2 4 11 22 43 86 175

Question 11

What is the square root of -1, -2, and -12?

Answer 11

i, 2i, 2i times the square root of 3

Question 12

What is i^2?

Answer 12

-1

Question 13

What are complex numbers made of?

Answer 13

real and imaginary numbers (ex: a +bi. a is real and b is imaginary

Question 14

What is i to the 1st, 2nd, 3rd, and 4th power?

Answer 14

i, -1, -i, 1

Question 15

How would you find i to the 103rd power?

Answer 15

find the remainder of 103/4 and count up (ex: remainder is 3 so it equals i to the 3rd or -i)

Question 16

What is the rational zero test?

Answer 16

every rational zero of a polynomial will have the form p/q where p is a factor of the constant and q is a factor of the leading coefficient

Question 17

What are the rational zeros of 2x^3 + 3x^2 - 8x +3?

Answer 17

Ps are +/- 1 and +/- 3
Qs are +/-1 and +/- 2
P/Qs are +/- 1 and +/- 3 and +/- 1/2 and +/- 3/2

Question 18

Write a function with the zeros of 4 and -3i

Answer 18

(x - 4)(x + 3i)(x - 3i)

If something is a polynomial with an irrational zero, it must have a pair of conjugates so they can cancel

Question 19

What is Descartes Rule of Signs?

Answer 19

The number of positive real zeros of a function is either equal to the number of variations in sign of f(x) or less than that number by an even integer
The number of negative real zeros of a function is either equal to that number of variations in sign of f(-x) of less than that number by an even integer

Question 20

What are the possible numbers of positive and negative real zeros of -2x^3 + 5x^2 - x + 8?

Answer 20

F(x) is 3 or 1 positive real zeros (- + - +)

F(-x) is 0 negative real zeros (+ + + +)

Question 21

What are the upper and lower bound rules?

Answer 21

When f(x) is divided by (x - c)
If c > 0 and each # is the last row is + it is an upper bound
If c

Question 22

What is a rational function and how would you find vertical and horizontal asymptotes?

Answer 22

VA- set the denominator equal to zero and solve

HA- (n degree of numerator and m degree of denominator) if n>m none, n=m leading coe/leading coe, if n

Question 23

How would you find the zeros or x-int of a rational function?

Answer 23

Set numerator equal to zero and solve, watch domain