Standard Form Formula
A standard form is a form of writing a given mathematical concept like an equation, number, or an expression in a form that follows certain rules. The process of writing a given mathematical concept like an equation, number, or an expression in the standard form follows certain rules. The standard form formula helps in finding out this general representation for different types of notation. Hence, we will be understanding how does standard form formula helps us.
What is Standard Form Formula?
We will be learning about the following standard form formula:
 Standard form formula of a polynomial
 Standard form formula of a linear equation
 Standard form formula of a quadratic equation
 Standard form formula of a line
Standard form formula of a polynomial:
The rules for writing a polynomial in standard form are very simple.
1. Write the terms in the descending order of their powers (also called as exponents).
2. Ensure the polynomial contains no like terms.
The standard form formula of a polynomial is:
\(a_nx^n + a_{n1}x^{n1}.....+a_0\)
Standard form formula of a linear equation:
The standard form formula of a linear equation is of the form:
A_{1 }x_{1} + A_{2 }x_{2 }+ A_{3 }x_{3 }+ ........ + A_{n }x_{n }= D
where A_{i} and D are integers.
A_{1}, A_{2}, A_{3},_{ } ........ A_{n }do not have any factors in common.
The standard form formula of a linear equation in two variables x and y is given by:
ax + by = c
where a, b and c are integers and the equation is in the simplest form, i.e. a, b, c do not have any factors in common.
Standard form formula of a quadratic equation:
The standard form formula of a quadratic equation is of the form:
ax^{2} + bx + c = 0 where a ≠ 0
where a, b, c are integers and a, b, c do not have any factors in common.
The standard form of a line
A linear equation geometrically represents a line.
Hence, the standard form of a line is the same as that of a linear equation.
Ax + By = C
We can also determine the slope of a given line.
If we come across an equation in a standard form that we are required to present graphically, we must convert it to slopeintercept form.
To do this, we must solve the equation for y.
For slope, we write the equation in the form: \(y = mx+c\)
Here \(m\) represents the slope of the line.
Let's look into some examples to understand the standard form formula.
Solved Examples Using Standard Form Formula

Example 1:Convert the following linear equation y = 3x + 4 into a standard form using the standard form formula.
Solution.
According to standard form formula of linear equation,
A_{1 }x_{1} +A_{2 }x_{2}+ A_{3 }x_{3 }+ ........ + A_{n }x_{n }= D
Given: y = 3x + 4
y  3x = 4 or 3x  y+ 4 = 0
3x + y = 4 or 3x  y = 4
Answer: Standard form of the given linear equation is 3x + y = 4 or 3x  y = 4

Example 2: Convert the following quadratic equation into standard form: \( \frac{1}{x} + x = 1\)
Solution.
\( \dfrac{1}{x} + x = 1\)
Multiplying x on both sides,
1 + x^{2 }= x
Shifting R.H.S. terms to L.H.S.,
x^{2}  x + 1 = 0
Answer: Standard form of the given quadratic equation is 2x^{2}  9x + 63 = 0