Math for College Algebra - Formulas for Test 1

College course 1105

Distance Formula

Midpoint Formula

You can put repeating decimals as your answer

False (write as fraction)

When given an endpoint and midpoint and asked to solve for the other midpoint, you should solve by…

1) Use the midpoint formula.

2) plug the X coordinate of the midpoint given into M (what equation equals).

3) plug the X coordinate of the endpoint given into X₁ (of the formula).

4) LEAVE X₂ BLANK AND SOLVE FOR X₂ by multiplying the denominator (2) by both sides of the equation and adding the constant to the other side. NOT DONE YET

5) plug the Y coordinate of the midpoint given into M (what equation equals).

6) plug the Y coordinate of the endpoint given into Y₁ (of the formula).

7) LEAVE Y₂ BLANK AND SOLVE FOR Y₂ by repeating the process from step 4

Pythagorean Theorem

C² = a² + b² where c is hypotenuse

Area of a Triangle

A = ½ bh

How to find perimeter

add up all sides

To find the X intercept…

set Y=0

To find the Y intercept…

set X=0

What are the 3 symmetries of a circle?

Symmetrical @ y-axis (x=0)

Symmetrical @ x-axis (y=0)

Symmetrical @ origin (0,0) or (Y=X)

How can you tell which axis something is symmetrical @?

By changing the signs and if the solution stays the same, it is symmetrical on that axis.

x-axis: (x,-y)

y-axis: (-x,y)

origin: (-x,-y)

*hint: similar concept to when finding an intercept

How to find 2 point of an equation

1) Create a table with X and Y

2) Put in values for X (like 1 and -1)

3) Plug X into given equation and solve for Y

Axis of symmetry is y-axis

axis of symmetry is x-axis

axis of symmetry is point of origin (0,0)

TWO Point slope formula

Slope Intercept Form

Point Slope Form

Standard Form

Positive slope

Negative slope

Undefined Slope

Slope is Zero

What formula would you use for “find the equation of the line that connects the 2 points”

y-y₁ = m(x-x₁)

A parabola is an equation with what powers?

2,4,6,8

What are the powers for this backwards S shaped graph?

3,5,7,9

Relation

Correspondence between 2 sets

Function

From X into Y is a relation that associates with each element of X and exactly one element of Y (VLT)

Given X=1, what is F(X)?

F(1) = (1)² —> always square to find answer

^{F(1) = 1}

Given (1,2),(3,-1),(-4,5) What’s the Domain?

{1,3,-4 }

Set interval notation

(-∞ ,+∞)

Set builder notation

{ x | x is all real numbers }

When looking at a solution set, how can it be a function?

It must not repeat x or y values

Difference quotient

(f/g)(x) = ?

x+1/x-3

Given (f/g)(x) find the domain

SET DENOMINATOR EQUAL TO ZERO x-3=0—> x=3

Even function rules

even power and symmetrical on y-axis

Odd function rules

odd power and symmetrical at the point of origin

Neither (odd nor even) function rules

if there are 2 powers and one is even and the other is odd. Not symmetrical.

What are zeros

x intercepts