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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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3.
Quadratic Functions
3.1
Characteristics of quadratic functions
3.2
Transformations of quadratic functions
3.3
Quadratic function in general form: y=ax2+bx+c
3.4
Quadratic function in vertex form: y = a(x−p)2+q
3.5
Completing the square
3.6
Converting from general to vertex form by completing the square
3.7
Shortcut: Vertex formula
3.8
Graphing parabolas for given quadratic functions
3.9
Finding the quadratic functions for given parabolas
3.10
Applications of quadratic functions