This chapter discusses quadratic equations, which are equations with the highest power of the variable being 2. A quadratic equation can be written in the standard form ax^2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to 0. The lesson provides examples of writing equations in standard form and identifying which equations are quadratic. Students are expected to be able to identify quadratic equations, write them in standard form, and apply the distributive property when solving them.

1. Chapter I<br />742950327660<br />This chapter deals with equations which are classified according to the highest power of its variable. An equation in the variable x whose highest power is 2 is called a quadratic equation. It will be observed here that variable a, b and c are real numbers and a cannot be 0.<br />TARGET SKILLS: At the end of this chapter, students are expected to:• identify quadratic equation;• discuss real numbers and standard form of the quadratic equation;• express quadratic equation in standard form; and• apply distributive property in solving quadratic equation.<br />Lesson 1<br />Identifying the quadratic equation<br /> OBJECTIVES:<br />At the end of this lesson, students are expected to:<br />define the quadratic equation;

2. discuss real numbers in quadratic equation; and

3. improve writing the standard form of the quadratic equation.Polynomials are classified according to the highest power of its variable. A first degree polynomial, like 2x + 5 is linear; a second degree polynomial, like x2 + 2 – 3 is quadratic; a third degree polynomial, like x3 + 4x2 – 3x + 12 is cubic.<br />Similarly, equation and inequalities are classified according to the highest power of its variable. An equation in the variable x whose highest power is two is called a quadratic equation. Some examples are x2 – 64, 4n2 = 25, 3x2 – 4x + 1 = 0.<br />An equation of the form ax2 + bx + c = 0, where a, b and c are constant and a not equal to 0, a id a quadratic equation.<br />Any quadratic equation can be written in the form ax2 + bx + c = 0. This is also called the standard form of the quadratic equation. Here, a, b and c are real numbers and a cannot be 0.<br />Example A. Express x2 = 8x in standard form<br /> x2 = 8x can be written as x2 - 8x = 0<br /> where a=1, b= ˉ8, and c=0.<br />Example B. Express x2 = 64 in standard form<br /> x2 = 64 can be written as x2 – 64 = 0<br /> where a=1. B=0, and c=ˉ64.<br />Example C. Express the fractional equation x = 1/x-3 as a quadratic equation.<br /> x = 1/x-3 <br /> x (x-3) = 1 multiply both sides by x-3<br /> x² - 3x = 1 using the distributive property<br /> x² - 3x - 1 = 0 a=1, b=ˉ3, c=ˉ1<br />Exercises: <br />Which of the following equations are quadratic?<br />1. 3x = x² - 5<br />2. 2x =1<br />3. x² = 25<br />4. 2x - 3 = x + 5<br />5. 5x – 2y = 0<br />-495300-779144Name: ___________________ Section: _______<br />Instructor: ________________ Date: _______ Rating: ____<br /> <br />Instruction: Write the following equations in the form ax2 + bx + c = 0, and give the value of a, b, and c.<br />X2 = 6x _____________________________________________<br />2x2 = 32 _____________________________________________ <br />3x2 = 5x – 1 _____________________________________________<br />10 = 3x – x2 _____________________________________________<br />(x + 2)2 = 9 _____________________________________________<br />4x2 = 64 _____________________________________________<br />-514350-7219371x+ x =5 _____________________________________________<br />x(x-3)-1=0 _____________________________________________<br />8x = x2 _____________________________________________<br /> 1x2 = 6 _____________________________________________<br />(x-3)2x=0 _____________________________________________<br />x2 = 32 _____________________________________________<br />x =1x+2 _____________________________________________ <br />x2 + 43 = 2x _____________________________________________<br />(x + 1)(x-3) = 6Define each of the following terms.<br />Quadratic equation<br />Standard form of a quadratic equation<br />Real numbers<br />Which of the following equations are quadratic?<br />4x = 2x2 – 6<br />3x = 1<br />5x2 = 30 <br />3x – 2 = 2x + 6<br />2x – 5y = 0<br />4x + 2x2 – 3x3 = 0<br /> 12x2 – x = 11<br />Write the following equations in the form ax2 + bx + c = 0, and give the values of a, b and c.<br />3x2 = 6x<br />3x2 = 32<br />2x2 = 5x – 1<br />12 = 4x – x2 <br />(x + 3)2 = 8<br />4x2 = 56<br />1/x + x = 6<br />x(x – 4) – 1 = 0<br />9x = x2 <br />10. (1/x)2 = 10<br />