WRITING QUADRATIC EQUATIONS IN STANDARD FORM

A quadratic equation is an equation of the form [beautiful math coming... please be patient]$\,ax^2 + bx + c = 0\,$, where $\,a \ne 0\,$.
The form [beautiful math coming... please be patient]$\,ax^2 + bx + c = 0\,$ is called the standard form of the quadratic equation.

Notice that standard form is not unique.
For example, [beautiful math coming... please be patient]$\,x^2 - x + 1 = 0\,$ can be written as the equivalent equation [beautiful math coming... please be patient]$\,-x^2 + x - 1 = 0\,$.
Also, [beautiful math coming... please be patient]$\,4x^2 - 2x + 2 = 0\,$ can be written as the equivalent equation [beautiful math coming... please be patient]$\,2x^2 - x + 1 = 0\,$.

In this exercise, all answers are reported in the form [beautiful math coming... please be patient]$\,ax^2 + bx + c = 0\,$ with [beautiful math coming... please be patient]$\,a > 0\,$,
and where the greatest common factor of all nonzero coefficients is 1.

In this exercise, you will practice writing quadratic equations in standard form.

EXAMPLES:
Question: Write [beautiful math coming... please be patient]$\,2x^2 = x + 4\,$ in standard form:
Answer: [beautiful math coming... please be patient]$\,2x^2 - x - 4 = 0\,$
Question: Write [beautiful math coming... please be patient]$\,3x = -x^2 + 7\,$ in standard form:
Answer: [beautiful math coming... please be patient]$\,x^2 + 3x - 7 = 0\,$
Question: Write [beautiful math coming... please be patient]$\,6x^2 - 6x = 12\,$ in standard form:
Answer: [beautiful math coming... please be patient]$\,x^2 -x - 2 = 0\,$
Question: Write [beautiful math coming... please be patient]$\,3x - 2 = 5x\,$ in standard form:
Answer: 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:
Solving Simple Quadratic Equations by Factoring

 
 
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
Write in standard form: