Converting from general to vertex form by completing the square
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Examples
Lessons
- 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 - 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 - 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 - 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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Topic Notes
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!
Basic Concepts
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