Blog 4: Learn Quadratic function with Ben

Math-160-002

Youwei Cheng

April 20^th 2015

Blog 4: Be the Professor

Topic of the lecture: Quadratic Function

Date: April 20^th 2015

·         Introduction

            Hi everyone, my name is Professor Cheng and you can call me Ben if you like. I’m glad to be your math teacher this semester. I hope we are going to have a fun time together through learning useful math knowledge and skills. Today I am going to teach you: the Quadratic Function.

·         What is Quadratic Function?

I believe all of you have learned linear function before. Quadratic function has a squared x instead of an x in linear function. So quadratic function is a function that can be described by an equation of the form f(x) = ax² + bx + c, where a ≠ 0.

Ø  a, b and c are known values. a can't be 0.

Ø  "x" is the variable or unknown.

·         Examples:

5x² + 2x + 4=0 is an example of a quadratic function. This is also a standard form.

·         Graph

Ø  Its graph is a parabola. When you kick a soccer ball, it arcs up into the air and comes down again.

·         How to solve it?

There are three ways to solve the quadratic equation:

Ø  Factoring

Ø  Complete the square

Ø  Using quadratic formula

I will teach you how to solve quadratic equation using these three methods next class.

·         Example in real life:

Ø  A ball is thrown straight up, from 5 m above the ground, with a velocity of 20 m/s. When does it hit the ground?

Solution:

The height starts at 5m: 5

It travels upward at 14 meters per second (20m/s): 20t

Gravity effect, slowing its speed by 5m/s per second (5 m/s): - 5t²

Add them up and the height h at any time t is:

h = 3 + 14t - 5t²

And the ball will hit the ground when the height is zero:

3 + 14t - 5t² = 0

Now you get a quadratic function!

·         Conclusion

As we can see from the example above, quadratic functions are very useful in real life. They are widely used in science, business, and engineering. Most of the objects we use every day, from cars to clocks, would not exist if someone, somewhere hadn't applied quadratic functions to their design.