Standard form

Standard form is method of representing complex equations into simpler form.In standard forms  we
can bring in the solutions easily
With out doing much calculations.
so we are using standard form for our
reference.


Standard form of a linear equation

The standard form of a linear equation helps us to represent the linear equation in the simplest form. The standard form of a linear equation is given by Ax+ By = C, where A, B and C are constants and A ≠ 0.

Example: -
Find the equation of the line passing through the points (6, 12) and (3, 7) and express it in the standard form.
Solution: -
We know that the line passing through two points (x1, y1) and (x2, y2) is given by
y - y1 = m (x - x1) where m is the slope of the line, which is given by                      m =  (y2 - y1)/(x2 - x1)
Given that the line passes through (x1, y1)  = (6, 12) and  (x2, y2) = (3 , 7).
Lets first find the slope.
Slope m = (y2 - y1)/(x2 - x1) = (7 - 12 )/(3 - 6) = -5/-3 = 5/3
Substituting in the equation of the line, we get
y - 12 = 5/3 (x - 6)
Cross multiplying we get
3y - 36 = 5x - 30
Adding 30 on both sides, we get
3y - 6 = 5x
subtracting 3y on both sides we get
5x - 3y = -6, which is the required equation.  Here A = 5, B = -3 and C = -6.


Standard form in algebra

Standard form in algebra refers to writing complex equations in simpler form.  The standard form of quadratic equation in algebra is given by ax2 + bx + c = 0, a ≠ 0.

Example: -
Write the quadratic equation in standard form.
7x = 5x2 - 8
Solution: -
We know that the standard form of the quadratic equation is given by ax2 + bx + c = 0, a ≠ 0.
Given equation is 7x = 5x2 - 8
To convert this to standard form, we take all terms to the right.
Subtracting 7x from both sides, we get
5x2 - 7x - 8 = 0, which is the required standard form

Standard form in math

Standard form in math refers to writing large numbers in simpler form. We write a number in the form x * 10y,where x is a decimal number with only one number before decimal.

Example: -
Write the number 356.479 in the standard form.
Solution: -
Given number is 356.479. we have to write this number in standard form.
In the standard form we write the number in the form x * 10y,where x is a decimal number with only one number before decimal.
That is 356.479 = 3.56479 x 102
So the standard form of 356.479 = 3.56479 x 102

Lets see how to write conic sections in standard form

If the center of the circle is at the point (h, k) and has radius of the circle is r, then the equation of the circle is given by (x - h)2+ (y - k)2= r2
This representation of the circle is called the standard form of the circle


The standard form of a parabola is given by y = ax2 + bx + c, a ≠ 0. It is the general quadratic equation.
If a is greater than 0, the parabola opens upwards and if a is less than 0, the parabola opens downwards.