# 2nd Degree Polynomial

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Equation / Last modified by KurtHeckman on 2018/06/07 16:04
y =
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vCalc.2nd Degree Polynomial
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The Second Degree Polynomial calculator computes the result of a second degree polynomial (y = a•x²+b•x +c).

INSTRUCTIONS:  Enter the following:

• a - the multiplicative constant for the term
• b - the multiplicative constant for the x term
• c - constant term
• x - the value to be substituted for x

Second Degree Polynomial (y): The calculator returns the value of y.

### DERIVATION

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:

1.    a*x^2
2.    b*x
3.   c

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

• where a is a constant multiplying the x^2 term
• where b is a constant multiplying the x^1 term (x to the first power is just x)
• where c is a constant multiplying the x^0 term (x to the zero power is just 1)

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

## EXAMPLES

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 can also be zero.  Technically, the 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.

•       ex. y = 5x^2 + 0x + 23 = 5x^2 + 23
•       ex. y = 2x^2 + 6.5x + 0 = 2x^2 + 6.5x

Here is an example of one of the constants, the b constant, being a negative multiplier:

•      ex. y = 3.7x^2 - 1.4x + 22.2
•      ex. y = 7x^2 - 4x + 2