Manitoba

Math

Grade 11 Pre-Calculus Mathematics (30S)

11. Analyze quadratic functions of the form y = a(x - p)² + q and determine characteristics of the corresponding graph

11.6 Completing the square

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Completing the square

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Grade 11 Pre-Calculus Mathematics (30S)

Develop algebraic and graphical reasoning through the study of relations

11. Analyze quadratic functions of the form y = a(x - p)² + q and determine characteristics of the corresponding graph

11.6 Completing the square

Completing the Square: Unlock the Power of Quadratic Equations

Master the art of completing the square to solve complex quadratic equations, find parabola vertices, and convert to vertex form. Boost your algebra skills and tackle real-world math problems with confidence.

What You'll Learn

Recognize when a trinomial forms a perfect square and factor it into binomial squared form

Apply the completing the square method to convert quadratics from general form to vertex form

Calculate the term needed to complete the square by halving the x coefficient and squaring it

Factor out coefficients from x² terms before completing the square

Identify the vertex and stretch factor of a parabola from vertex form equations

What You'll Practice

Converting trinomials into perfect square binomial form

Completing the square with positive and negative coefficients

Factoring out coefficients including fractions before completing the square

Transforming general form quadratics into vertex form to identify the vertex

Why This Matters

Completing the square is essential for graphing quadratics quickly and understanding their key features. This technique lets you convert any quadratic into vertex form, making it easy to identify the vertex, axis of symmetry, and transformationsskills you'll need throughout algebra, precalculus, and calculus.

Before You Start — Make Sure You Can:

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2Quadratic function in vertex form: y = a(x-p)^2 + q

This Unit Includes

8 Video lessons

Practice exercises

Learning resources

Skills

Completing the Square

Quadratic Equations

Vertex Form

Perfect Square Trinomials

Factoring

Parabolas

Algebra

MB Curriculum Aligned