Introduction/Focus Students will be able to write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
The teacher will briefly discuss with the class yesterdays lesson on how to solve linear equations. On the board, the teacher will write the equation , if solve for . The teacher will have a student say to him how to solve the problem and what steps are taken. The teacher will then write another equation , if solve for . The teacher will choose another student to state how to solve the problem step by step.
1. After the review, the teacher will write on the board the equation , if solve for . The teacher will state that they have never seen this type of problem before and that they will be learning on how to solve problems like these. A question the teacher will ask is if anyone knows how to solve a type of problem like this. After all ideas have been presented, the teacher will state that for this type of problem factoring can be used. The problem can be broken down into and setting the problem can now be solved to see that . The teacher will also write that if any equation is in the form and if , then one can use the form to solve for .
1. The teacher will write on the board , if solve for . The teacher will then ask the class if this equation is in the form stated above. After the class acknowledges the question, the teacher will then go around the room to each student asking several questions such as what do the letters equal, how would one try to solve the problem, and to plug in the values to see if this is indeed the correct answer.
2. The teacher will draw a coordinate graph on the board. The teacher will then ask the class what the values they solved tell us about the graph of this equation. In other words, the class will state the points that they solved.
3. The teacher will then write another problem on the board . Again, the teacher will go around the room asking how to solve this problem asking what they think the values for are, how one would use the quadratic equation, and just to check with oneself to see if the answer is right. The teacher will also make another coordinate graph asking the class what the values they solved for meant and how one would put these values onto the graph.
1. The teacher will hand out a worksheet to the class that will be for homework.
2. The teacher will then ask the class questions to summarize the class. Some of these questions include, but are not limited to asking what the form has to be in order to be considered a quadratic equation, what two ways can one solve a quadratic equation for given that , and what do these values represent in terms of the graph. The teacher will also write on the board the equation where and one needs to solve for . The teacher will state for the class to think about this equation and to determine how one can use the quadratic formula to solve it.
1. The teacher will ask questions to review the ideas of the class stated above.
2. The worksheet that the teacher passed out will be homework the class. The homework will be collected the next day and will be graded based on the student’s understanding.
Solve each of the quadratic problems for when . In addition, graph each set of equations.