


Quadratic PolynomialsxinterceptsThe points on the graph cut by the xaxis (that is, y = 0) are called the xintercepts. For a general parabola given by y = ax^{2}
+ bx+ c , these might not exist, as the parabola may
lie wholly above or below the xaxis. We consider a few easy cases: Case 1: c = 0, ax^{2} + bx = 0 Note: x is a common factor. Thus x(ax + b) = 0. Hence either x = 0 or x = b/a. Example 3.Study a few more examples.
Exercise 3.Now try a few on your own. Case 2: b = 0, ax^{2} + c = 0 We rewrite the equation as Or Example 4.Here are some worked examples. The notation sqrt stands for and is common notation used in programs such as Excel and MATLAB. Exercise 4.Feeling confident? Good. Try a few of then on your own. Case 3: y = (ax  b)(cx  d) In this situation, the xintercepts are (b/a, 0) and (d/c, 0). Exercise 5.
Case 4: y = ax^{2} + bx + c Regardless of the values of a, b and c, we can use the quadratic formula to find the xintercepts. We will look at this in a later section titled "The Quadratic Formula".
Note: If the xintercepts exist and are distinct then the xcoordinate of the vertex is the midpoint of the intercepts.
Example 5.Draw the parabola given by the equation y = x^{2} − 6x. The xintercepts are (0, 0) and (6, 0). Hence the vertex is situated at x = 6/2 = 3. And y = 3^{2} – 6(3) = 9. The vertex is (3, 9).
Exercise 6.When using the applet, enter the function you wish to be drawn on the function line and click on new function. The applet starts with f(x) = x^2 + 2x. To look at a particular point on the graph (the vertex for example) enter the value of x in the box provided and the point will be highlighted by a grey '+'.
Can't see the above java applet? Click here to see how to enable Java on your web browser. (This applet is based on free Java applets from JavaMath )
Example 6.Draw the parabola given by the equation y = x^{2} − 4. The xintercepts are (2, 0) and (2, 0), hence the vertex is (0, 4). The graph is
Exercise 7.When using the applet, enter the function you wish to be drawn on the function line and click on new function. The applet starts with f(x) = x^2 + 1. To look at a particular point on the graph (the vertex for example) enter the value of x in the box provided and the point will be highlighted by a grey '+'.
Can't see the above java applet? Click here to see how to enable Java on your web browser. (This applet is based on free Java applets from JavaMath )
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