Mathematics for Chemistry/Plotting graphs
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[edit] The properties of graphs
The most basic relationship between two variables x and y is a straight line, a linear relationship.
y = mx + 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 = ax2 + bx + 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.
[edit] Practice
Plot x2 − 1 between -3 and +2 in units of 1.
Plot x2 + 3x between -4 and +1 in units of 1.
Plot 2x3 − 5x2 − 12x between -5 and +4 in units of 1.
