In these sections, we will explore a class of nonlinear functions called quadratic functions. One place you might encounter a quadratic function is when solving problems that involve chemical equilibrium.

For example, a key enzyme in cells is adenylate kinase, which catalyzes the transfer of a phosphate group (PO₄^-) from adenosine triphosphate (ATP) to adenosine monophosphate (AMP). The result of this reaction is the formation of two molecules of adenosine diphosphate (ADP) by the following reaction,

ATP + AMP ↔ 2 ADP.

The equilibrium constant (K_eq ) for this reaction is calculated as shown below:

where [ATP] is the concentration of ATP, [ADP] is the concentration of ADP, and [AMP] is the concentration of AMP. If you were given initial concentrations of ATP and AMP, could you calculate how much ADP you would have once the reaction reaches equilibrium? You can if you understand quadratic functions.

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In the next section we explore the basics of quadratic functions.

The basics