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Standard form is a common way of representing any notation/equation. The Standard Form Formula represents the general acceptance form of an equation. For a polynomial, the standard form can be represented as writing the terms with higher-order first to the lower order, and the coefficients of each term should be in integral form. The formula to represent an equation in standard form depends on the degree of an equation.

### Standard Form Formula for Linear Equations

The standard form of a linear equation with two variables x and y is ax + by = c where a, b, and c are integers. Let’s consider a linear equation which consists of more than two variables i.e., x1, x2, x3, ….,xn and A1, A2, A3,…., An are coefficients of each term then standard form formula of the equation is given by,

(A1)x1 + (A2)x2 + (A3)x3 + …. + (An)xn = c

### Standard Form Formula for Quadratic Equations

The standard form of the second-degree quadratic equation for a single variable x is ax2 + bx + c = 0 where a, b, c are integers and a ≠ 0. For n degree equations the standard form is (A1)xn + (A2)xn-1 + (A3)xn-2 + …. + (An)x + c = 0 where A1, A2, A3, … An are coefficients, n is the degree of the equation, x is a single variable and c is the constant numeric term. Many geometrical figures have standard form formulas which are listed below,

• The standard form formula for a circle is (x-h)2 + (y-k)2 = r2 where (h, k) is the center of a circle and r is the radius.
• The standard form formula for an ellipse is given by( x2/a2) + (y2/b2) = 1 where a, b are lengths of semi-major and semi- minor axis.
• The standard form formula for a parabola is (x-h)2 = 4p(y-k).
• The standard form formula for a hyperbola is ((x – x0)2/a2) – ((y – y0)2/b2) = 1 where (x0, y0) are center point and a, b are lengths of semi major and semi minor axis.

### Sample Questions

Question 1: Convert the given linear/straight line equation y – 4 = -2x in standard form.

Solution:

Given linear equation

y – 4 = -2x

The standard form of linear equation is ax + by = c

2x + y – 4 = 0

2x + y = 4

So the standard form of given equation is 2x + y = 4.

Question 2: Convert the given straight line equation 7y = -2x + 3 in standard form.

Solution:

Given linear equation

7y = -2x + 3

The standard form of linear equation is ax + by = c

7y + 2x = 3

2x + 7y = 3

So the standard form of given equation is 2x + 7y = 3.

Question 3: Convert the given quadratic equation 2x – 9 = 7x2 in standard form.

Solution:

2x – 9 = 7x2

The standard form of quadratic equation is ax2 + bx + c = 0

2x = 7x2 + 9

7x2 – 2x + 9 = 0

So the standard form of given equation is 7x2 – 2x + 9 = 0.

Question 4: Convert the given quadratic equation (2x/7)-1 = 2x2 in standard form.

Solution:

Given equation,

(2x/7) – 1 = 2x2

(2x-7(1))/7 = 2x2

(2x-7)/7 = 2x2

2x – 7 = 7(2x2)

2x – 7 = 14x2

14x2 – 2x + 7 = 0

So the standard form of given equation is 14x2 – 2x + 7 = 0

Question 5: Convert the given  equation (2x3/x) + 4 = 2x in standard form.

Solution:

Given equation,

(2x3/x) + 4 = 2x

One of the x in x3 is cancelled by the x in denominator to form x2

2x2 + 4 = 2x

2x2 – 2x + 4 = 0

The above equation is further simplified to give x2 – x + 2 = 0

So the standard form of given equation is x2 – x + 2 = 0

Question 6: Convert the given quadratic equation into standard form (3/x) – 2x = 5.

Solution:

Given equation,

(3/x) – 2x = 5

(3-2x(x))/x = 5

(3-2x2)/x = 5

3-2x2 = 5x

2x2 + 5x – 3 = 0

So the standard form of given quadratic equation is 2x2 + 5x – 3 = 0.

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