Study Sheet

Question 1

Factor: a²-b²

Answer 1

(a+b)(a-b)

Question 2

Factor: a³+b³

Answer 2

(a+b)(a²-ab+b²)

Question 3

Factor: a³-b³

Answer 3

(a-b)(a²+ab+b²)

Question 4

Slope Formula

Answer 4

Question 5

At an x intercept, what is y equal to?

Answer 5

0

Question 6

At a y intercept, what is x equal to?

Answer 6

0

Question 7

What is the equation for the standard form of a line?

Answer 7

Ax+By=C

Note:

m = -A/B

x intercept = C/A

y intercept = C/B

Question 8

What is the equation for a line in slope-intercept form?

Answer 8

y=mx+b

Note:

m = slope

b = y intercept

Question 9

What is the equation of a line in point-slope form?

Answer 9

(y-y₁)=m(x-x₁)

Note:

(x₁, y₁) is a point on the line

Question 10

Parallel lines have the same…

Answer 10

Slope

Note:

All vertical lines are parallel.

Question 11

Perpendicular lines have slopes which are…

Answer 11

Negative reciprocals of each other.

Note:

Their product is -1.

Question 12

What are two lines with the same slope, but different y intercept called?

Answer 12

Parallel

Question 13

What are two lines with the same slope, and same y intercept called?

Answer 13

Coincident

Question 14

What are two lines that are negative recipricals called?

Answer 14

Perpendicular

Question 15

What are two lines with different slopes, but not negative reciprocals called?

Answer 15

Oblique

Question 16

Distance Formula

Answer 16

Question 17

Midpoint Formula

Answer 17

Note:

(x₁,y₁) and (x₂,y₂) are points.

Question 18

Quadratic Formula

Note:

If ax²+bx+c=0

Answer 18

Question 19

What is the equation of the discriminant?

What does the discriminant do?

Answer 19

b²-4ac

It determines the number and nature of the roots.

Question 20

If the value of the discrimnant is positive then how many roots of what nature are there?

Answer 20

2 real

Question 21

If the value of the discriminant is zero then how many roots of what nature are there?

Answer 21

1 real (double root)

Question 22

If the value of the discriminant is negative then how many roots of what nature are there?

Answer 22

2 imaginary or complex

Question 23

How do you find the sum of the roots in a discriminant?

Answer 23

-b/a

Question 24

How do you find the product of the roots in a discriminant?

Answer 24

c/a

Question 25

a^m+aⁿ=

Answer 25

a^m+n

Question 26

(a^m)ⁿ=

Answer 26

a^mn

Question 27

a^-n=

Answer 27

1/aⁿ

Question 28

1/a^-n=

Answer 28

aⁿ

Question 29

(a/b)^m=

Answer 29

a^m/b^m

Question 30

a^m/aⁿ=

Answer 30

a^m-n

Question 31

a^1/n=

Answer 31

Question 32

a^m/n=

Answer 32

Question 33

General form for a conic section:

Answer 33

Ax²+By²+Cxy+Dx+Ey+F=0

Question 34

In which conic section is the locus (set) of all point a given distance (radius) from a given point (center)?

Answer 34

Circle

Question 35

General form for a circle:

Answer 35

Ax²+Ay²+Dx+Ey+F=0 Note: A=B, C=0

Question 36

(h, k) form for a circle:

Answer 36

(x-h)²+(y-h)²=r² Note: Center- (h,k) Radius- r

Question 37

Identify this conic section.

Answer 37

Parabola

Question 38

In which conic section are the locus of all points whose distance from a given point (focus) and a given line (directrix) equal?

Answer 38

Parabola

Question 39

Quadratic in x: axis of symetry parallel to the x-axis - Which ways can it open?

Answer 39

Up or Down

Question 40

General form for a parabola (in x):

Answer 40

Ax²+Dx+Ey+F=0 y=ax²+bx+c Note: A and E are nonzero. a is nonzero.

Question 41

Vertex form for a parabola (in x):

Answer 41

(x-h)²=4p(y-k) Note: Focus: (h,k+p) Directrix: x=k-p

Question 42

Quadratic in y: axis of symmetry parallel to the x-axis - Which ways can it open?

Answer 42

Right or Left

Question 43

General form for a parabola (in y):

Answer 43

By²+Dx+Ey+F=0 x=ay²+by+c Note: B and D are nonzero. a is nonzero.

Question 44

Vertex form for a parabola (in y):

Answer 44

(y-k)²=4p(x-h) Note: Focus: (h + p,k) Directrix: x=h-p

Question 45

Vertex of a parabola:

Answer 45

(h,k)

Question 46

The distance from the vertex to Focus in a parabola:

Answer 46

p=a/2

Question 47

The distance from the vertex to Directrix in a parabola:

Answer 47

p

Question 48

The length of the latus rectum in a parabola:

Answer 48

4p