Quadratic Function
A function of the form , where and are constants, and , is called a quadratic function. Such functions often arise in applied mathematics. For instance, the height of a projectile is a quadratic function of time, the velocity of blood flow is a quadratic function of a distance from the center of the blood vessel; and the force exerted by the wind on the blades of a windpowered generated is a quadratic function of the wind speed.
The simple quadratic function is the square function , whose graph is a curve. The graph of is obtained from the graph of by vertical stretching, if , or flattening, if. Furthermore, the graph of for negative values of is obtained by reflecting the graph across the xaxis. Figure 1 shows the graph of for various values of .

Figure 1 , where , and 
The graph of equation of the form is are examples of curves called parabolas. These parabolas are systemic about the yaxis; they open upward and have a lowest point at if , Figure 2 (a), and they open downward and have a highest point at (0, 0) if , Figure 2 (b). The highest or lowest point of the graph of is called vertex of the parabola, and its line symmetry is called the axis of symmetry or simply the axis of the parabola.


Figure 2 (a) , 
Figure 2 (b) , 