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WRITING QUADRATIC EQUATIONS IN STANDARD FORM
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A quadratic equation is an equation of the form
ax2 + bx + c = 0 , where a is not equal to 0 .
The form ax2 + bx + c = 0 is called the standard form of the quadratic equation.
Notice that standard form is not unique.
For example, x2 - x + 1 = 0 can be written as the equivalent equation
-x2 + x - 1 = 0 .
Also, 4x2 - 2x + 2 = 0 can be written as the equivalent equation
2x2 - x + 1 = 0 .
In this exercise, all answers are reported in the form ax2 + 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 2x2 = x + 4 in standard form:
Answer: 2x2 - x - 4 = 0
Question: Write 3x = -x2 + 7 in standard form:
Answer: x2 + 3x - 7 = 0
Question: Write 6x2 - 6x = 12 in standard form:
Answer: x2 - x - 2 = 0
Question: Write 3x - 2 = 5x in standard form:
Answer: not a quadratic equation
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.