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# Mathematic Mind Map

My mathematic presentation on algerbraic functions (Year 8)

by

Tweet## Conan Tran

on 19 August 2015#### Transcript of Mathematic Mind Map

Linear

Function Quadratic

Function 5 ways

to solve Straight

Line Parabola 1 way

to solve Exponential Equality

and

Inequality

Equality:

= Inequality:

<=, >=, =, <, > Linear:

Dash line

+ shading Quadratic:

Dash line

+ Shading y=ax^2+bx+c Point of Slope:

m = slope

b = y-intercept Graphing Standard form:

Ax+By=C Factoring Graphing Completing

the Square Axis of Symmetry

x= number (x-coordinate) Axis of symmetry

x= a number Solid line < or <=:

Below or right

> or >=:

Left or above Discriminant Vertex Ordered pair X-coordinate Y-coordinate X-intercept

Y-intercept Finding

X-coordinate

-b/2a In quadratic function X-intercept are also

Solutions

Roots

Zeros Perfect Square form;

No x term

and c is rational Function is hard

to factor or at all.

No other solutions. Using if x^2 term is 1

and hard to factor. Using if you have

Graphing Calculotor. To find how many

solutions are there!

b^2-4(a)(c) Tips:

Term of x^2 (+)

Graph go up

Term of x^2 (-)

Graph go down. Algebraic

Function Exponential

Function Discovery about Functions

And

Their

Graphs < or <=:

Term of x^2(Positive):

outside

Term of x^2(Negative)

: inside > or >=:

Term of x^2(Positive):

inside

Term of x^2(Negative)

: ouside Square Root Quadratic

Formula 4 ways

to solve y=mx+b Rate of change or Slope

Vertical change

/Horizontal change How are those applied? Real-life problem 1 Systems of

Linear

Function 3 solutions

of system

of linear function Graphing Substitution Elimination The line approaches

the x-axis

but not cross or touch y=a.b^x Replacing f(x) = Results

a = initial

b = ratio, rate of change

x = number of periods (how many times it repeat) Suppose a restaurant has 2 staffs at first. After 3 months, the guests come crowder so the number of staffs double.

Question: how many staffs will there be after 2 years? Problem 1 is solving by Exponential Function Real-life problem 2 A market-observer records that a price of a product is about $60 and it could attract 1000 customers. That employee also notices that if the price reduces $1, it could attract more 60 customers. Suppose M(x) is the highest profit that product can make and count as: -(2a)x+b. Question: What is M(x)? Problem 2 is solving by Quadratic Function

Full transcriptFunction Quadratic

Function 5 ways

to solve Straight

Line Parabola 1 way

to solve Exponential Equality

and

Inequality

Equality:

= Inequality:

<=, >=, =, <, > Linear:

Dash line

+ shading Quadratic:

Dash line

+ Shading y=ax^2+bx+c Point of Slope:

m = slope

b = y-intercept Graphing Standard form:

Ax+By=C Factoring Graphing Completing

the Square Axis of Symmetry

x= number (x-coordinate) Axis of symmetry

x= a number Solid line < or <=:

Below or right

> or >=:

Left or above Discriminant Vertex Ordered pair X-coordinate Y-coordinate X-intercept

Y-intercept Finding

X-coordinate

-b/2a In quadratic function X-intercept are also

Solutions

Roots

Zeros Perfect Square form;

No x term

and c is rational Function is hard

to factor or at all.

No other solutions. Using if x^2 term is 1

and hard to factor. Using if you have

Graphing Calculotor. To find how many

solutions are there!

b^2-4(a)(c) Tips:

Term of x^2 (+)

Graph go up

Term of x^2 (-)

Graph go down. Algebraic

Function Exponential

Function Discovery about Functions

And

Their

Graphs < or <=:

Term of x^2(Positive):

outside

Term of x^2(Negative)

: inside > or >=:

Term of x^2(Positive):

inside

Term of x^2(Negative)

: ouside Square Root Quadratic

Formula 4 ways

to solve y=mx+b Rate of change or Slope

Vertical change

/Horizontal change How are those applied? Real-life problem 1 Systems of

Linear

Function 3 solutions

of system

of linear function Graphing Substitution Elimination The line approaches

the x-axis

but not cross or touch y=a.b^x Replacing f(x) = Results

a = initial

b = ratio, rate of change

x = number of periods (how many times it repeat) Suppose a restaurant has 2 staffs at first. After 3 months, the guests come crowder so the number of staffs double.

Question: how many staffs will there be after 2 years? Problem 1 is solving by Exponential Function Real-life problem 2 A market-observer records that a price of a product is about $60 and it could attract 1000 customers. That employee also notices that if the price reduces $1, it could attract more 60 customers. Suppose M(x) is the highest profit that product can make and count as: -(2a)x+b. Question: What is M(x)? Problem 2 is solving by Quadratic Function