Algebra Tutorials! Saturday 16th of February

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 Dependent Variable

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## What the Standard Form of a Quadratic can tell you about the graph

The graphs of quadratic equations come in two varieties: smiling and frowning (see Figure 1, ). The standard form of a quadratic equation:

y = a Â· x 2 + b Â· x + c,

can tell you whether a given graph will smile or frown. If the number (or coefficient), a, multiplying the x 2 is positive then the quadratic is smiling. If the number a is negative then the quadratic is frowning.

Figure 1(a): The graph of a smiling quaratic equation opens upwards and outwards, like a smiling mouth.

Figure 1(b): The graph of a frowning quaratic equation opens downwards and outwards, like an unhappy mouth.

The appearance of the quadratic equation (smiling or frowning) is controlled by the sign of the number a.

 Sign of the number a in the quadratic equation Appearance of the graph of the quadratic equation Negative Frowning Positive Smiling

Table 1: Effect of sign of a on appearance of quadratic graph.