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Converting from general to vertex form by completing the square
- Intro Lesson14:51
- Lesson: 14:58
- Lesson: 25:17
- Lesson: 33:48
- Lesson: 45:10
Converting from general to vertex form by completing the square
Basic Concepts: Factoring polynomials: ax2+bx+c, Quadratic function in general form: y=ax2+bx+c, Quadratic function in vertex form: y = a(x−p)2+q, Completing the square
Related Concepts: Solving quadratic equations by completing the square, Graphing reciprocals of quadratic functions, System of quadratic-quadratic equations, Graphing quadratic inequalities in two variables
Lessons
Step-by- step approach:
1. isolate X's on one side of the equation
2. factor out the leading coefficient of X2
3. "completing the square"
• X-side: inside the bracket, add (half of the coefficient of X)2
• Y-side: add [ leading coefficient (half of the coefficient of X)2 ]
4. clean up
• X-side: convert to perfect-square form
• Y-side: clean up the algebra
5. (optional)
If necessary, determine the vertex now by setting both sides of the equation equal to ZERO.
6. move the constant term from the Y-side to the X-side, and we have a quadratic function in vertex form!
1. isolate X's on one side of the equation
2. factor out the leading coefficient of X2
3. "completing the square"
• X-side: inside the bracket, add (half of the coefficient of X)2
• Y-side: add [ leading coefficient (half of the coefficient of X)2 ]
4. clean up
• X-side: convert to perfect-square form
• Y-side: clean up the algebra
5. (optional)
If necessary, determine the vertex now by setting both sides of the equation equal to ZERO.
6. move the constant term from the Y-side to the X-side, and we have a quadratic function in vertex form!
- IntroductionIntroduction to completing the square using the "6-step approach": y=2x2−12x+10
- 1.Completing the square with NO COEFFICIENT in front of the x2 term
Convert a quadratic function from general form to vertex form by completing the square.
y=x2+3x−1 - 2.Completing the square with a NEGATIVE COEFFICIENT in front of the x2 term
Convert a quadratic function from general form to vertex form by completing the square.
y=−3x2−60x−50 - 3.Completing the square with a RATIONAL COEFFICIENT in front of the x2 term
Convert a quadratic function from general form to vertex form by completing the square.
y=21x2+x−25 - 4.Completing the square with NO CONSTANT TERM
Convert a quadratic function from general form to vertex form by completing the square.
y=5x−x2
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14.
Quadratic Functions
14.1
Characteristics of quadratic functions
14.2
Transformations of quadratic functions
14.3
Quadratic function in general form: y=ax2+bx+c
14.4
Quadratic function in vertex form: y = a(x−p)2+q
14.5
Completing the square
14.6
Converting from general to vertex form by completing the square
14.7
Shortcut: Vertex formula
14.8
Graphing parabolas for given quadratic functions
14.9
Finding the quadratic functions for given parabolas
14.10
Applications of quadratic functions
Don't just watch, practice makes perfect
Converting from general to vertex form by completing the square
Don't just watch, practice makes perfect.
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