## 2. The quadratic function explored

The simplest quadratic equation would look like:

y = x^{2}

More generally, a quadratic equation will have the form:

y = ax^{2} + bx + c

where a, b and c are the **parameters** or **coefficients** of the equation. The parameters can be positive or negative, and a must be non-zero, whilst b and/or c can be zero.

The parabola described by the quadratic equation is a consequence of the squared term. Take the simple example at the start of this section, y = x^{2}. It is clear that when x = 0, y also equals zero. When x = 2, y = 4, but when x = -2 again y = 4. A plot of this function looks like this:

If the parameter a has a negative value, the parabola is inverted. For instance, the equation y = -x^{2} looks like this:

Section 4 explores the effects of changing other parameters in the quadratic equation, to produce a variety of parabolas.