IDENTIFYING QUADRATIC EQUATIONS
DEFINITION quadratic equation
Let $\,a\,$, $\,b\,$ and $\,c\,$ be real numbers, with $\,a\ne 0\,$.
A quadratic equation is an equation of the form: [beautiful math coming... please be patient] $$ax^2 + bx + c = 0$$

Important notes about the definition:

So, to check if an equation is a quadratic equation,
you want to make two passes through it (both sides):

EXAMPLES:

In this exercise, you will practice identifying quadratic equations.

Question: Is $\,x^2 = x + 4\,$ a quadratic equation?
Solution:
Does it have an $\,x^2\,$ term?   Check!
Anything other than $\,x\,$ terms or constant terms?   Nope.   Check!
YES, it is a quadratic equation.
Question: Is $\,3x - 4 = x + 1\,$ a quadratic equation?
Solution:
Does it have an $\,x^2\,$ term?   Nope.
So, it's not a quadratic equation.
Question: Is $\,x - 2x^2 = 1 + x^5\,$ a quadratic equation?
Solution:
Does it have an $\,x^2\,$ term?   Check!
Anything other than $\,x\,$ terms or constant terms?   Oops.
Quadratic equations are not allowed to have an $\,x^5\,$ term.
So, it's not a quadratic equation.
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Writing Quadratic Equations in Standard Form

 
 
Is this a quadratic equation?
YES
NO
 
    
(an even number, please)