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Definition
Completing the square is an algebraic method used to transform a quadratic equation of the form:
into a perfect square trinomial, making it easier to solve or rewrite in vertex form.
The process involves manipulating the equation to express it as:
Summary
Concept Explanation:
- The method rewrites a quadratic expression into a perfect square plus or minus a constant.
- It is used to simplify solving quadratic equations and to understand their properties.
Procedure:
- Divide by a (if a≠1)
- Take half of the coefficient of x, square it, and add it to both sides.
- Factor the resulting trinomial into a square.
- Solve for x if needed.
Applications:
- Solving quadratic equations
- Deriving the quadratic formula
- Analyzing the vertex and axis of symmetry of parabolas
Benefits:
- Provides a deeper understanding of quadratic functions.
- Offers a direct way to find the vertex (h,k) of a parabola.
Completing the Square Math Activities
This is a fantastic bundle which includes 10 activities with answer guides about Completing the Square. All our worksheets are completely editable so can be tailored for your curriculum and target audience.
Resource Examples
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Worksheets Activities Included
- Perfect Square Recognition
- Completing the Square – Basic Practice
- Completing the Square with Constants
- Solving Quadratic Equations
- Quadratic with Leading Coefficient
- Converting to Vertex Form
- Finding the Vertex
- Application Problem
- Create & Solve
- Mixed Practice Challenge