SLC S22W6//Graphing and Conic sections

drhira (76)in #algebra-s22w6 • 8 days ago

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

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.