MDME: MANUFACTURING, DESIGN, MECHANICAL ENGINEERING

# POLYNOMIALS

Polynomials are equations with multiple powers of a variable (like x). In this chapter we are only dealing with polynomials of order 2 (up to x squared only). These are also called quadratics or binomials and they plot a parabola.

Smartboard Notes:     Blank

Worked Problems on Video: Blank

### Parabolas (Polynomials of power 2 - binomials)

A quadratic equation can be plotted when it is put into the form:

#### y = ax2 + bx +c

Where;

x = x coordinate

y = y coordinate

The three coefficients a,b & c change the shape and position of the parabola.

Download this Excel file to see what happens when these variables are changed.

Polynomial graphs in Excel

(Or see the Parabola Plotter below).

##### What happens if you change coefficient a?

A larger a makes the parabola steeper, a smaller a makes it flatter.

A negative a gives an upside-down parabola

##### What happens if you change coefficient c?

The coefficient c raises or lowers the parabola in the y direction.

##### What happens if you change coefficient b?

The coefficient b is kind of weird. It tries to move the parabola sideways, but it also raises and lowers the parabola at the same time. So if you want to move the parabola sideways you need to change coefficient b as well as adjust the vertical position with c.

##### What happens if you combine changes to all coefficients a,b & c?

Now we get a pretty random mixture of changing the shape with a, changing the vertical position with c, and changing the horizontal & vertical position with b.

### Parabola Plotter

y = ax2 + bx + c This has roots, at x1= and x2=
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