For some constants a, b, and c, the standard form* is ...
ax^2 + bx + c = 0
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It is nice if the leading coefficient (a) is positive, but that is not required.
The main ideas are that ...
Powers of the variable are descending
All of the non-zero terms are on the left side of the equal sign
Like terms are combined
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* This is the <em>standard form</em> for a quadratic. For other kinds of equations, when the expression is equal to zero, this would be called "general form."