The lesson plan introduces how to solve quadratic inequalities in one unknown using a graphical method for equations with two distinct real roots. It involves showing examples of graphs of quadratic functions and identifying the intervals where the corresponding y-values meet the inequality condition. Students are given practice questions to sketch quadratic graphs and solve inequalities based on the graphs. The lesson concludes with a brief review of the topic taught.

1. Lesson Plan<br />Date: 23rd Nov, 2010 (Tue)<br />Time: 40 mins<br />Class: F.4H<br />Number of students: 37<br />Topic: More About Inequalities<br />Quadratic Inequalities in one unknown<br />Basic knowledge:<br />Graphs of quadratic equation<br />Solving the quadratic equations by factor method<br />Learning objectives:<br />After completing this lesson, students will be able to<br />solve quadratic inequalities in one unknown by graphical method.<br />(For the quadratic equations which have two distinct real roots)<br />Teaching tools:<br />Book, worksheet, computer, projector<br />Time:Teaching procedureTeaching strategyTools3’RevisionTell the students that they have learnt how to solve all types of linear inequalities in one unknown.Ask them if they have any questions about linear inequalities in one unknown. 10’Introduce how to find the solutions of quadratic inequalities from the graph (for two distinct real roots)Show the graphs of two quadratic functions by the computer.E.g. y=x+3x-2Ask the students to consider the open interval -3<x<2, what are the corresponding values of y?They should able to answer that all values of y in this interval are smaller than zero.Then we can say, the solutions of the inequality x+3x-2<0 are -3<x<2.How about for x<-3 or x>2, what are the corresponding values of y?They should able to answer that all values of y in those regions are greater than zero.Then we can say, the solutions of the inequality x+3x-2>0 are x<-3 or x>2.So we can also find the solutions by considering the values of y. If we would like to find y=x+3x-2>0, we just consider the region above the x-axis to find the corresponding x.Consider one more example:We multiply -1 in the previous example.i.e. y=-x+3x-2Ask the students to consider the open interval -3<x<2, what are the corresponding values of y?They should able to answer that all values of y in this interval are greater than zero.Then we can say, the solutions of the inequality x+3x-2>0 are -3<x<2.How about for x<-3 or x>2, what are the corresponding values of y?They should able to answer that all values of y in those regions are smaller than zero.Then we can say, the solutions of the inequality x+3x-2<0 are x<-3 or x>2.So we can also find the solutions by considering the values of y. If we would like to find y=-x+3x-2>0, we just consider the region above the x-axis to find the corresponding x. Com-puter6’Test the students to see whether they can solve the quadratic inequalities by giving graphsAsk the students to do question number 1 on the worksheet.Walk around to examine how they have learnt and answer them if they have any questions.Work-sheet8’The procedure of solving quadratic inequalities by graphical method(for the case of the quadratic which have two distinct real roots)In general, we can solve the quadratic inequalities by the graphical method with the following steps.Sketch the graph of y=ax2+bx+c and mark the x-intercepts.Brief revision on sketching quadratic graphWhen a>0, the graph opens upwardsWhen a<0, the graph opens downwardsFor y=ax-b(cx-d), the x-intercepts should be (ba,0) and (dc,0).According to the sketch, find the intervals of x at which the corresponding values of y meet the requirement of the inequality given. Show an example to the students,e.g. y=-2x2+9x+5y=-2x2-9x-5y=-2x+1(x-5)∵a<0, ∴ opens downwardAnd the x-intercepts are (-12,0) and (5,0)Then we can sketch the graph.10’Test the students to see whether they can sketch the graph and solve the quadratic inequalities by the sketched graphs(two distinct real roots)Ask the students to do question number 2 on the worksheet.Walk around to examine how they have learnt and answer them if they have any questions.Work-sheet3’ConclusionGive them a brief revision on today’s topic to remind them what they have learnt today.How to find the solutions from the graphHow to sketch the quadratic graphAsk the students to do 7D #5-8 in bookbook<br />