A-level Mathematics/MEI/C1/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.

Graph of the equation y=x²

Sketching

Graph of the equation y=x⁴

Graph of the equation y=x⁶

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.