How to write a quadratic equation,polynomial, or number in standard form?
A decimal number, an equation, or a polynomial may be read, written, and understood in standard form. Consider writing the distance between the earth and moon. Is it possible to read 384400000 meter? What about a distance of 3.8 × 108 m?
This is where we use standard form to understand the type of numbers that can be very difficult to read or write. The same is true for small numbers such as an atom’s mass. Standard form is not only used for decimal numbers. It can also be used forpolynomials, equations that are linear, quadratic equations, and numbers in decimal form.
But the big question is; how to write a quadratic equation, a linear equation, a polynomial, or a number in standard form?If you find it difficult to do it on your own, keep reading because we will clarify how to transform an equation, number, or polynomial into standard form.
What is standard form?
According to Wikipedia,
Scientific notation or standard from is a method of stating numbers that are too small or too large to be easily written in decimal form. It may be referred to as scientific form or standard form in the United Kingdom.
We use a multiplication sign and the number 10 to express a number in standard from. In later sections, we will explain the method to convert any number or equation in standard form in detail.
Method: How to write in standard from?
There are different rules for each type of conversion. For example, to convert a number into standard form, we use a few rules. The same rules may not apply for converting a polynomial in standard or scientific form.
In this section, we will explain each method one-by-one. Checkout write in standard form calculator before we move to the methods of converting a number or equation in standard from.
Let’s first understand how to convert a linear equation in standard from.
Writing a linear equation in standard form
A linear equation in standard form can be expressed as,
Ax + By = C
To convert a linear equation into standard form, write the equation in the above format. Here are the main points to remember when converting a linear equation to standard form.
- A cannot be negative.
- A, and B both cannot be zero.
- The values of A, B, and C must be integers.
Let’s put these rules into practice with a linear equation.
Convert the following equation into standard (scientific) form.
3y = 2x + 5
- Place 2x on the left side of the equation.
– 2x + 3y = 5
- To remove the negative sign with the variable x, multiply the whole equation by -1.
2x – 3y = -5
This equation has now been transformed into regular form. In this case, we can write the values as:
A = 2 B = 3 C = -5
Writing a number in standard form
We’ll use an example and see how to write numbers in scientific form.
A micro biology scientific is conducting experiments to figure out the sizes of various species lying under the surface of earth.He will then present the findings to a committee having 6 persons on board.
If the size of a specie is 0.000000345 meter, don’t you think it would be very inconvenient for the scientist to present the number by reading it or to work with it in the lab? Of course it is.Let’s convert this number in standard form for the ease of scientist and the committee. Follow the steps given below.
- Delete all leading zeroes and pass the decimal after the first non-zero number.
- Count the cumulative number of digits from which the decimal has been moved. In this case, we shifted the decimal to the right by 7 places.
- Put the multiplication sign and 10 next to the number we got in the first step.
= 3.45 x 10
- To get the standard form, raise -7 as power of 10.
When lifting a number as a power of 10, use a negative sign with power if the digit has been shifted from left to right. The power (exponent) should be positive if you moved the decimal from right to left.
3.45 x 10-7
We can now use this number without hesitation, despite the fact that it is very small. A standard form calculator could be very handy in this case.
Writing a polynomial in standard form
The idea behind the standard form of a polynomial is to start with the component with the highest degree. The variable’s exponent is referred to as its degree. Let us use an example again to explain the method of converting a polynomial in standard form.
Convert the following polynomial into standard form.
8x2 + 5x6 – 3 + 2x5 + 6x4
Using the degree of each element, we can arrange the equation in descending order. In this case, the highest degree term is 5x6.
5x6 + 2x5 + 6x4+ 8x2– 3
Writing a quadratic equation in Standard Form
A quadratic equation can be expressed in standard form as shown below.
Ax2 + bx + c = 0
To understand the method of converting a quadratic equation into standard form, let’s use an examples like we used in above methods.
Convert the following quadratic equation into standard form.
x(10 + x) = 4
- Solve the left hand side first.
x(10 + x)
Multiply the variable xwith the expression (10 + x).
10x + x2
Rewrite it as:
x2 + 10x = 4
- Take the constant 4 on the left side of the equation.
x2 + 10x – 4 = 0
x2 + 10x – 4 = 0 is the standard form of the given quadratic equation x(10 + x) = 4.
We can write the values of variables and constants as:
A = 1, B = 10, and C = -4.
The methodsexplained in this post may vary depending on the type of the equation. The standard form of a linear equation cannot be obtained using the rules of a quadratic equation. So, use these methods accordingly for each type of equation or number in order to correctly write them in standard form.