Lesson 4 Quadratic Inequalities part ii

Introduction
In the previous lesson, we saw how we could use a graph to make comparisons between two [color=#0000ff]functions[/color], one of which being [color=#0000ff]quadratic[/color], by finding the [color=#0000ff]points of intersection[/color].[br][br]It is not always practical to plot [color=#0000ff]accurate[/color] graphs of functions, particularly when the points of intersection are [color=#0000ff]non-integer[/color].  Sometimes it will be necessary to [color=#0000ff]rearrange[/color] our inequality so that we can draw comparisons with the line y=0 (the [math]x[/math][color=#0000ff]-intercepts[/color]) since the co-ordinates here are obtainable by finding the [color=#0000ff]roots[/color] of the equation.[br][br]It is important to note that the general shape of a quadratic changes depending on whether the co-efficient of [math]x^2[/math] is positive or negative.[br][br]                                               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[/img]
Using the quadratic formula calculator to find the x-intercepts of your graph
To help you find the [math]x[/math]-intercepts (roots) of your quadratic function, you may wish to use the quadratic calculator.  You should enter the values for a, b and c where your function is in the form:[br]                                                              [math]ax^2+bx+c[/math][br]
Example
If we look at the example from last lesson: [math]x^2+3x+1<1-x[/math], rather than solve by plotting both functions, lets rearrange the inequality using inverse operations so that we are looking to find where: [br]                                                                         [math]x^2+4x<0[/math].[br][br]I can now produce a sketch of the general shape of the parabola, and by finding the solutions either by factorising, using the quadratic formula, or using the calculator above I am now able to label my               [br][math]x[/math]-intercepts.[br][br][img]data:image/png;base64,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[/img][br]So my roughly sketched graph would look like this:[br]                                               [img]data:image/png;base64,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[/img][br]and I can easily identify for which region the quadratic is below the line [math]y=0[/math], it is, as we previously found, all values of [math]x[/math], -4<[math]x[/math]<0
Task
There are two different worksheets for this task, depending on whether or not you are able to rearrange using inverse operations.  If you have not learnt this skill yet, please complete the task which does not require you to do so.
No rearranging required
Requires rearranging

Information: Lesson 4 Quadratic Inequalities part ii