• Quadratic functions
An algebraic expression of the form ax²+ bx + c is called a quadratic function of x.Graph of the quadratic function ax²+ bx + c (a≠ 0)
Procedure:
1. Make a table of corresponding values for x and the function.
2. Plot these points, on a pair of x, f(x) axes.
3. Draw a smooth curve joining the plotted points.
The graph of a quadratic function is parabola. The point at which its direction changes is called its turning point. It is more commonly called the vertex of the parabola.
The graph of the function is concave upwards when a> 0 and concave downwards when a< 0.
NOTE:
Studying the nature and character of the roots of a quadratic by graphing:
The graph give below illustrate the following cases.
Real roots
Case 1: a > 0 Equal roots
Complex roots
Real roots
Case 2: a< 0 Equal roots
Complex roots
a) If the graph cuts the x-axis, the roots of the equation will be real and unequal. Their values will be given by the abscissa of the points of intersection of the graph and the x-axis.
b) If the graph is tangents to the x-axis, the roots are real and equal.
c) If the graph has no points in common with the x-axis, the roots of the equation are imaginary and can not be determined from the graph.
