Chapter 2

Question 1

Finding y-intercept in a parabola

Answer 1

when x = 0

Question 2

Finding x-intercept in a parabola

Answer 2

when y = 0 (there can be multiple)

Question 3

Finding axis of symmetry in a parabola

Answer 3

x in the vertex or -b/2a or h

Question 4

Finding vertex in a parabola

Answer 4

to find x: axis of sym
to find y: f(aos)
(x, y) or (h, k)

Question 5

standard -> vertex

Answer 5

complete the square

Question 6

complete the square

Answer 6

y = x² - 4x - 5

1. set equation to zero: 0 = x² - 4x - 5
2. move the constant term: 5 = x² - 4x
3. take half of the coefficient of x and square it: 4x->2->4
4. add to both sides: x² - 4x + 4 = 5 + 4
5. rewrite left side as squared: (x - 2)x² = 9
6. take the square root of both sides: x - 2 = ± 3
7. isolate x: x = ±3 + 2

Question 7

completing the square if x² has a coefficient

Answer 7

y = 4x²+20x+25

1. set equal to zero: 0 = 4x²+20x+25
2. divide the polynomial by 4: x² + 5x + 25/4 = 0
3. move the constant term: x² + 5x = -25/4
4. take half of the coefficient of x and square it: 5->5/2->25/4
5. add to both sides: x² + 5x + 25/4= -25/4 + 25/4 -> x² + 5x + 25/4 = 0
6. rewrite left side as squared: (x + 5/2)² = 0
7. take the square root of both sides: x + 5/2 = 0
8. isolate x: x = -5/2

Question 8

vertex -> standard

Answer 8

y = 2(x - 3)² + 4

1. expand the squared binomial: 2(x-3)(x-3) + 4
2. foil: 2(x² -6x + 9) + 4
3. distribute: 2x² - 12x + 18 + 4
4. combine: 2x² - 12x + 22

Question 9

Long division

Answer 9

fill in the non x’s with 0

Question 10

Synthetic division

Answer 10

fill in the non x’s with 0

Question 11

two arrows pointing the same direction

Answer 11

even

Question 12

two arrows pointing in opposite directions

Answer 12

odd

Question 13

even pointing up

Answer 13

positive x

Question 14

even pointing down

Answer 14

negative x

Question 15

odd starting down ending up

Answer 15

positive x

Question 16

odd starting up ending down

Answer 16

negative x

Question 17

if a line goes straight through x-axis

Answer 17

1 root

Question 18

if a line just touches then bounces off the x-axis

Answer 18

2 roots

Question 19

if a line goes through the x-axis but holds on the x-axis longer

Answer 19

3 roots

Question 20

i

Answer 20

√-1

Question 21

i²

Answer 21

-1

Question 22

i³

Answer 22

-i or -√-1

Question 23

i⁴

Answer 23

1

Question 24

how to check what i to a high power is

Answer 24

i⁷³⁵

1. divide the power by 4: 183.75
2. multiple the whole number by 4: 732
3. subtract to find remainder: 3
4. remainder = power: i³ or -i

Note: if the remainder is 0 it means to the power of 4

Question 25

How to solve complex numbers

Answer 25

if the denominator has a complex number multiply both the top and bottom by the reciprocal of the bottom. then solve.

Question 26

Finding roots

Answer 26

use synthetic division (L/F)

Question 27

Last/First

Answer 27

Factors of the last number / Factors of the first number

Question 28

Miracle formula

Answer 28

x² - sumx + productx

Question 29

Solving rational

Answer 29

FACTOR FIRST

Question 30

Finding y-intercept in a rational

Answer 30

set x equal to zero

Question 31

Finding x-intercept in a rational

Answer 31

set the numerator equal to zero (can be multiple)

Question 32

Finding vertical asymptote in a rational

Answer 32

set the denominator equal to zero (can be multiple)

Question 33

Finding horizontal/slant asymptote in a rational

Answer 33

1. Look at the highest powered x on the numerator and denominator * If the denominator's x is to a higher power: y = 0 * if the numerator and denominators x is to the same power: numerator x's coefficent / denominator x's coeffiecent * if the numerator's x is to a higher power: there is no horizontal asymptote, but a slant or oblique asymptote

Question 34

Finding slant asymptote in a rational

Answer 34

1. Divide the num by the dem using long division 2. Ignore the remainder 3. y = the answer (ignoring rem)

Question 35

Hole in rational

Answer 35

after factoring, if any binomials in the denominator and numerator are the same = hole