Mathematics for Chemistry/Plotting graphs

The properties of graphs

The most basic relationship between two variables $x$ and $y$ is a straight line, a linear relationship.

$y = {\rm m} x + {\rm c}$

The variable $m$ is the gradient and $c$ is a constant which gives the intercept. The equations can be more complex than this including higher powers of $x$, such as

$y = {\rm a} x^2 + {\rm b} x + {\rm c}$

This is called a quadratic equation and it follows a shape called a parabola. High powers of $x$ can occur giving cubic, quartic and quintic equations. In general, as the power is increased, the line mapping the variables wiggles more, often cutting the $x$-axis several times.

Practice

Plot $x^2 - 1$ between -3 and +2 in units of 1.

Plot $x^2 + 3 x$ between -4 and +1 in units of 1.

Plot $2 x^3 -5 x^2 - 12 x$ between -5 and +4 in units of 1.