Writing Quadratic Equations in Standard Form

A quadratic equation is an equation of the form $\,ax^2 + bx + c = 0\,$, where $\,a \ne 0\,$.
The form $\,ax^2 + bx + c = 0\,$ is called the standard form of the quadratic equation.

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

In this exercise, all answers are reported in the form $\,ax^2 + bx + c = 0\,$ with $\,a > 0\,$,
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

$\,2x^2 = x + 4\,$ in standard form:

Answer:

$\,2x^2 - x - 4 = 0\,$

Question: Write

$\,3x = -x^2 + 7\,$ in standard form:

Answer:

$\,x^2 + 3x - 7 = 0\,$

Question: Write

$\,6x^2 - 6x = 12\,$ in standard form:

Answer:

$\,x^2 -x - 2 = 0\,$

Question: Write

$\,3x - 2 = 5x\,$ 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