SLC S22W6//Graphing and Conic sections

in #algebra-s22w6last month

Hello friends how are you doing today I am here to take part in the challenge that is quite informative and challenging.

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Differentiate between quadratic and exponential functions with examples and general forms of each!

I will try to explain few differentiation between quadratic and exponential functions, with suitable examples and general forms as well.

If we see quadratic Function with General Form
I will explain the easy general form of a quadratic function is as follows.

f(x) = ax^1 + bx + c

where:

The constants are - a, b, and c and in case of

  • a ≠ 0 (if a = 0, it's a linear function as well.

Example is as described

f(x) = 4x^1 + 2x - 3

Few characteristics are as follows.

The quadratic functions

  • It's in parabolic shape which may be u-shaped or inverted U-shaped.

  • There is single vertex

  • The presence of symmetry at vertical axis

  • The upward or downward graph 📉 📈 is present

Exponential Functions
Here is general form of exponential function

If f(x) = ab^x in this case constants are - a and b hence

  • b > 0 and b ≠ 1 (if b = 1, it's called linear function

Example
f(x) = 4^x

Few characteristics are as follows.

Exponential functions are given below.

  • There is rapid increase or decrease in value as the value of x is changed.

  • There is horizontal asymptote in more simply it means the graph touching the horizontal line)

  • There is no vertex nor axis of symmetry

  • There is always positive positive

Task 2

I will try to explain examples from daily life for more easy understanding.

First of all I will explain the exponential Functions with examples.

If we see the virus Growth: the growth of virus can be just doubled in number within every few hours. If we have 10 virus initially, then the number of x hours would be modeled with the exponential function.

The second example is the Investment Growth: If I have invested $100 having a 5% annual interest rate, my investment will grow exponentially with over time.

Now Quadratic Functions

For example if I am Throwing a Ball in upward direction it's upwards height will have quadratic path, the ball would move up, peaked and obviously then come back.

Then I would like to Designing a Garden in case I have rectangular garden having fixed amount of fence I will use quadratic function to finding optimal numbers of dimensions.

Task 3

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Task 4

Scenario 1

![IMG_20250123_112221.jpg](

Scenario 2

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It's all about my today's post.

I would like to invite my friends @m-fdo, @jannat12 and @iqrarana786 to take part in the challenge.

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Thank you for participating in s22 w6 learning challange!


CriteriaStatus
Plagiarism 🆓
AI 🆓
CategoryRemark
Task 11.35/1.5
Task 21.4/1.5
Task 32.85/3
Task 42.85/3
Post quality0.8/1
Total grade9.25/10

Teacher's Observation

Task 1 reviewYou have accurately discuss about exponential functions as well as quadratic functions and you described their characteristics but you have not explain their practical examples with along algebraic examples as well as you can also add little touch of creativity by adding graphical illustration!
Task 2 reviewViral growth and investment growth can really be considered as practical examples of exponential functions and on the other hand throwing a ball and designing a garden also considered real world example of quadratic equation so you explained them accurately but you can explain it little more!
Task 3 reviewYou have accurately find out for equation of circle according to centre and radius! You are also accurate in solving for X where you have implemented quadratic formula accurately but your theoratical explanation can enhance your concepts which you can share here little more!
Task 4 reviewIn this task if I talk about scenerio number 1 then you have graph equation I have provided,find out focal length of paraboloid as well as find out for equation of directrix!If I talk about scenario number two then you are accurate in graphing this equation, finding out maximum ball height and in sharing time which ball takes to reach to ground but overall you need to explain both scenarios step by step more in theory than solving it in steps!

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Good luck 🤞

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