Let’s Think About It
Travis found the following equation in his math book.
It is an equation to calculate velocity. In fact, it is a function. Being an avid sports player, Travis was very interested in figuring out how to use the equation, but he isn’t even sure what kind of a function it is. Can you identify this function?
In this concept, you will learn to recognize a quadratic function as an equation in two variables with a specific form.
Guidance
A parabola is a U shaped figure whose equation is a quadratic equation. Let’s start with quadratic equations and standard form.
To graph a quadratic equation, you need input values, oftentimes
A function is a relation that assigns exactly one value of the domain to each value of the range.
So, when you say quadratic function, you are referring to any function that can be written in the form
Why can’t ‘
If the ‘
Let’s take a look at some examples.
Identify if the following equations are quadratic functions. If they are, place them in standard form and identify ‘
1.
Yes, it is a quadratic function.
The standard form is
2.
Yes, it is a quadratic function.
The standard form is
3.
Yes, it is a quadratic function.
The standard form is
4.
With this function, you have to rewrite it into standard form. Standard form would have the
The function is not a quadratic function because if you subtract
Guided Practice
Is this function a quadratic function? If so, write it in standard form.
First, you have to get the
Next, divide both sides by 3.
The answer is that this is a quadratic function and the standard form is
Examples
Example 1
Identify whether or not the function is a quadratic function.
In standard form
Example 2
Identify whether or not the function is a quadratic function.
In standard form
Example 3
Identify whether or not the function is a quadratic function.
In standard form
Follow Up
Remember the function?
Is the function
This is a quadratic function because “
Video Review
https://www.youtube.com/watch?v=CuPgmA7ytWA
Explore More
Identify whether the following equations are quadratic functions. If they are, identify the ‘

y=3x2−x+4 
y=2x2+4 
2y=4x2+4 
3y=6x2+12 
4y=2x2−12 
3y−1=6x2+11 
2y+2=2x2+4 
y+2x2=2x2+4 
y−2x2=2x2+4 
y=2x2−3x+4 
y=4x−18+x2 
y+x2−6=x2+4x−5 
3y+3=9x2−12x 
6y=3x5+3x4+6x+−18 
4y+3x=8x2+3x−12