Mathematics for Chemistry/Plotting graphs

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The properties of graphs[edit]

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.


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.