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Thu, 14 Aug 2014 09:37:38 GMT狠狠撸Share feed for 狠狠撸shows by User: LenieZapataQuadratic equations
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quadraticequations-140814093738-phpapp02 Quadratic Equations
In One Variable
1. Quadratic Equation
an equation of the form
ax2 + bx + c = 0
where a, b, and c are real numbers
2.Types of Quadratic Equations
Complete Quadratic
3x2 + 5x + 6 = 0
Incomplete/Pure Quadratic Equation
3x2 - 6 = 0
3.Solving an Incomplete Quadratic
4.Example 1. Solve: x2 鈥� 4 = 0
Solution:
x2 鈥� 4 = 0
x2 = 4
鈭歺虏 = 鈭�4
x = 卤 2
5.Example 2. Solve: 5x虏 - 11 = 49
Solution:
5x虏 - 11 = 49
5x虏 = 49 + 11
5x虏 = 60
x虏 = 12
x = 卤鈭�12
x = 卤2鈭�3
6.Solving Quadratic Equation
7.By Factoring
Place all terms in the left member of the equation, so that the right member is zero.
Factor the left member.
Set each factor that contains the unknown equal to zero.
Solve each of the simple equations thus formed.
Check the answers by substituting them in the original equation.
8.Example: x虏 = 6x - 8
Solution:
x虏 = 6x 鈥� 8
x虏 - 6x + 8 = 0
(x 鈥� 4)(x 鈥� 2) = 0
x 鈥� 4 = 0 | x 鈥� 2 = 0
x = 4 x = 2
9.By Completing the Square
Write the equation with the variable terms in the left member and the constant term in the right member.
If the coefficient of x虏 is not 1, divide every term by this coefficient so as to make the coefficient of x虏 equal to 1.
Take one-half the coefficient of x, square this quantity, and add the result to both members.
Find the square root of both members, placing a 卤 sign before the square root of the right member.
Solve the resulting equation for x.
10.Example: x虏 - 8x + 7 = 0
11.By Quadratic Formula
Example: 3x虏 - 2x - 7 = 0
12.Solve the following:
1. x虏 - 15x 鈥� 56 = 0
2. 7x虏 = 2x + 6
3. 9x虏 - 3x + 8 = 0
4. 8x虏 + 9x -144 = 0
5. 2x虏 - 3 + 12x
13.Activity:
Solve the following quadratic formula.
By Factoring By Quadratic Formula
1. x虏 - 5x + 6 = 0 1. x虏 - 7x + 6 = 0
2. 3 x虏 = x + 2 2. 10 x虏 - 13x 鈥� 3 = 0
3. 2 x虏 - 11x + 12 = 0 3. x (5x 鈥� 4) = 2
By Completing the Square
1. x虏 + 6x + 5 = 0
2. x虏 - 8x + 3 = 0
3. 2 x虏 + 3x 鈥� 5 = 0
]]>
Quadratic Equations
In One Variable
1. Quadratic Equation
an equation of the form
ax2 + bx + c = 0
where a, b, and c are real numbers
2.Types of Quadratic Equations
Complete Quadratic
3x2 + 5x + 6 = 0
Incomplete/Pure Quadratic Equation
3x2 - 6 = 0
3.Solving an Incomplete Quadratic
4.Example 1. Solve: x2 鈥� 4 = 0
Solution:
x2 鈥� 4 = 0
x2 = 4
鈭歺虏 = 鈭�4
x = 卤 2
5.Example 2. Solve: 5x虏 - 11 = 49
Solution:
5x虏 - 11 = 49
5x虏 = 49 + 11
5x虏 = 60
x虏 = 12
x = 卤鈭�12
x = 卤2鈭�3
6.Solving Quadratic Equation
7.By Factoring
Place all terms in the left member of the equation, so that the right member is zero.
Factor the left member.
Set each factor that contains the unknown equal to zero.
Solve each of the simple equations thus formed.
Check the answers by substituting them in the original equation.
8.Example: x虏 = 6x - 8
Solution:
x虏 = 6x 鈥� 8
x虏 - 6x + 8 = 0
(x 鈥� 4)(x 鈥� 2) = 0
x 鈥� 4 = 0 | x 鈥� 2 = 0
x = 4 x = 2
9.By Completing the Square
Write the equation with the variable terms in the left member and the constant term in the right member.
If the coefficient of x虏 is not 1, divide every term by this coefficient so as to make the coefficient of x虏 equal to 1.
Take one-half the coefficient of x, square this quantity, and add the result to both members.
Find the square root of both members, placing a 卤 sign before the square root of the right member.
Solve the resulting equation for x.
10.Example: x虏 - 8x + 7 = 0
11.By Quadratic Formula
Example: 3x虏 - 2x - 7 = 0
12.Solve the following:
1. x虏 - 15x 鈥� 56 = 0
2. 7x虏 = 2x + 6
3. 9x虏 - 3x + 8 = 0
4. 8x虏 + 9x -144 = 0
5. 2x虏 - 3 + 12x
13.Activity:
Solve the following quadratic formula.
By Factoring By Quadratic Formula
1. x虏 - 5x + 6 = 0 1. x虏 - 7x + 6 = 0
2. 3 x虏 = x + 2 2. 10 x虏 - 13x 鈥� 3 = 0
3. 2 x虏 - 11x + 12 = 0 3. x (5x 鈥� 4) = 2
By Completing the Square
1. x虏 + 6x + 5 = 0
2. x虏 - 8x + 3 = 0
3. 2 x虏 + 3x 鈥� 5 = 0
]]>
Thu, 14 Aug 2014 09:37:38 GMT/LenieZapata/quadratic-equations-37993419LenieZapata@slideshare.net(LenieZapata)Quadratic equationsLenieZapataQuadratic Equations
In One Variable
1. Quadratic Equation
an equation of the form
ax2 + bx + c = 0
where a, b, and c are real numbers
2.Types of Quadratic Equations
Complete Quadratic
3x2 + 5x + 6 = 0
Incomplete/Pure Quadratic Equation
3x2 - 6 = 0
3.Solving an Incomplete Quadratic
4.Example 1. Solve: x2 鈥� 4 = 0
Solution:
x2 鈥� 4 = 0
x2 = 4
鈭歺虏 = 鈭�4
x = 卤 2
5.Example 2. Solve: 5x虏 - 11 = 49
Solution:
5x虏 - 11 = 49
5x虏 = 49 + 11
5x虏 = 60
x虏 = 12
x = 卤鈭�12
x = 卤2鈭�3
6.Solving Quadratic Equation
7.By Factoring
Place all terms in the left member of the equation, so that the right member is zero.
Factor the left member.
Set each factor that contains the unknown equal to zero.
Solve each of the simple equations thus formed.
Check the answers by substituting them in the original equation.
8.Example: x虏 = 6x - 8
Solution:
x虏 = 6x 鈥� 8
x虏 - 6x + 8 = 0
(x 鈥� 4)(x 鈥� 2) = 0
x 鈥� 4 = 0 | x 鈥� 2 = 0
x = 4 x = 2
9.By Completing the Square
Write the equation with the variable terms in the left member and the constant term in the right member.
If the coefficient of x虏 is not 1, divide every term by this coefficient so as to make the coefficient of x虏 equal to 1.
Take one-half the coefficient of x, square this quantity, and add the result to both members.
Find the square root of both members, placing a 卤 sign before the square root of the right member.
Solve the resulting equation for x.
10.Example: x虏 - 8x + 7 = 0
11.By Quadratic Formula
Example: 3x虏 - 2x - 7 = 0
12.Solve the following:
1. x虏 - 15x 鈥� 56 = 0
2. 7x虏 = 2x + 6
3. 9x虏 - 3x + 8 = 0
4. 8x虏 + 9x -144 = 0
5. 2x虏 - 3 + 12x
13.Activity:
Solve the following quadratic formula.
By Factoring By Quadratic Formula
1. x虏 - 5x + 6 = 0 1. x虏 - 7x + 6 = 0
2. 3 x虏 = x + 2 2. 10 x虏 - 13x 鈥� 3 = 0
3. 2 x虏 - 11x + 12 = 0 3. x (5x 鈥� 4) = 2
By Completing the Square
1. x虏 + 6x + 5 = 0
2. x虏 - 8x + 3 = 0
3. 2 x虏 + 3x 鈥� 5 = 0
<img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/quadraticequations-140814093738-phpapp02-thumbnail.jpg?width=120&height=120&fit=bounds" /><br> Quadratic Equations
In One Variable
1. Quadratic Equation
an equation of the form
ax2 + bx + c = 0
where a, b, and c are real numbers
2.Types of Quadratic Equations
Complete Quadratic
3x2 + 5x + 6 = 0
Incomplete/Pure Quadratic Equation
3x2 - 6 = 0
3.Solving an Incomplete Quadratic
4.Example 1. Solve: x2 鈥� 4 = 0
Solution:
x2 鈥� 4 = 0
x2 = 4
鈭歺虏 = 鈭�4
x = 卤 2
5.Example 2. Solve: 5x虏 - 11 = 49
Solution:
5x虏 - 11 = 49
5x虏 = 49 + 11
5x虏 = 60
x虏 = 12
x = 卤鈭�12
x = 卤2鈭�3
6.Solving Quadratic Equation
7.By Factoring
Place all terms in the left member of the equation, so that the right member is zero.
Factor the left member.
Set each factor that contains the unknown equal to zero.
Solve each of the simple equations thus formed.
Check the answers by substituting them in the original equation.
8.Example: x虏 = 6x - 8
Solution:
x虏 = 6x 鈥� 8
x虏 - 6x + 8 = 0
(x 鈥� 4)(x 鈥� 2) = 0
x 鈥� 4 = 0 | x 鈥� 2 = 0
x = 4 x = 2
9.By Completing the Square
Write the equation with the variable terms in the left member and the constant term in the right member.
If the coefficient of x虏 is not 1, divide every term by this coefficient so as to make the coefficient of x虏 equal to 1.
Take one-half the coefficient of x, square this quantity, and add the result to both members.
Find the square root of both members, placing a 卤 sign before the square root of the right member.
Solve the resulting equation for x.
10.Example: x虏 - 8x + 7 = 0
11.By Quadratic Formula
Example: 3x虏 - 2x - 7 = 0
12.Solve the following:
1. x虏 - 15x 鈥� 56 = 0
2. 7x虏 = 2x + 6
3. 9x虏 - 3x + 8 = 0
4. 8x虏 + 9x -144 = 0
5. 2x虏 - 3 + 12x
13.Activity:
Solve the following quadratic formula.
By Factoring By Quadratic Formula
1. x虏 - 5x + 6 = 0 1. x虏 - 7x + 6 = 0
2. 3 x虏 = x + 2 2. 10 x虏 - 13x 鈥� 3 = 0
3. 2 x虏 - 11x + 12 = 0 3. x (5x 鈥� 4) = 2
By Completing the Square
1. x虏 + 6x + 5 = 0
2. x虏 - 8x + 3 = 0
3. 2 x虏 + 3x 鈥� 5 = 0