A-level Mathematics/MEI/C1/Polynomials

Polynomials

polynomials are equations of the type axⁿ + bx^(n-1) + ... + c. In Core 1 you would be expected to be able to sketch and solve them. you only need to worry about positive powers of x for C1.

Sketching

To sketch a function you need to know:

Crossing points with both axis
whether the graph is above or below the axis between crossing points.
the general shape of the graph.

As we can see by looking to the right graphs of an even power are a "U" shaped curve. with greater powers having a longer "flat" section between 1 and -1

A graph has a limited number of turning points. This is 1 less than the highest power.

An equation with an odd power follows the same rule but will have a curvy shape starting at the bottom going through zero and then going off the top of the screen. I recommend that you use a graphing program like Geogebra to visualise these graphs.

Remember if the highest power has a coefficient of -1 then the curve will be upside down.

Solving

TBC - soon hopefully.