The Second Degree Polynomial calculator computes the result of a second degree polynomial (y = a•x²+b•x +c).
INSTRUCTIONS: Enter the following:
Second Degree Polynomial (y): The calculator returns the value of y.
A second degree polynomial is an equation of the form:
`y = ax^2 + bx + c` (showing the multiplications explicitly: `y = a*x^2 + b*x + c`)
In this simple algebraic form there are three additive terms shown on the right of the equation:
The equation is called "second degree" because it has an `x^2` term. If it also had an `x^3` term in it, it would be called a third degree polynomial.
Note that the three terms could be thought of as each term having a multiplying constant: a, b, and c
So, the form of the second degree polynomial could be re-written more explicitly to be:
`y = a*x^2 + b*x^1 + c*x^0`
We can make up examples values of a, b, and c to form an infinite number of variations on a second degree polynomial. The multiplicative constants, a, b, and c, can have integer or decimal values:
ex. `y = 5x^2 + 7x + 23` ; and if `x = 3`, `y = 89`
ex. `y = 3.7x^2 + 0.4x + 22.2` ; and if `x = 6.5`, `y = 181.125`
The multiplicative constants for b and c can also be zero. Technically, the a constant can't be zero if the equation is to be called a "second degree polynomial" but this brings up an interesting point: a lower degree polynomial is only a higher degree polynomial with all the higher order terms having multiplicative constants equal to zero. `a*x^2 + b*x + c = 0*x^5 + 0*x^4 + 0*x^3 + a*x^2 + b*x + c`
Here are two examples of the b and the c constants being zero.
Here is an example of one of the constants, the b constant, being a negative multiplier: