• Mathematical Methods
  • Year 11

The Quadratic Polynomial

approx. 7 hrs

4 topics

18 concepts

Develop greater understanding of The Quadratic Polynomial and advance into Year 12 with confidence.

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The Quadratic Polynomial is an essential part of the Year 11 Mathematical Methods course, as outlined in the Australian curriculum.  In this program, we work with students to develop the skills required to select algebraic techniques and solve quadratic functions, find the roots of a polynomial, and determine other key properties of quadratic functions. We also show how these relate to the parabolic curve.

Topics & Concepts We Cover

This learning program is made up of the following 4 topics, broken down into 18 concepts.

  • Sketch Quadratic Polynomials 8 concepts

    1. Select the appropriate factorising method to solve a given quadratic equation

    2. Sketching the quadratic function from the quadratic formula

    3. Sketching the quadratic function from the completed square

    4. Identify and use features of parabolas and their equations to assist in sketching quadratic relationships

    5. Find the vertex of a parabola

    6. Determine concavity of a parabola

    7. Find the axis of symmetry of a parabola

    8. Identify the x and y intercepts of a parabola

  • Nature of Roots 4 concepts

    1. Negative definite expressions defined by the discriminant

    2. Positive definite expressions defined by the discriminant

    3. Indefinite expressions defined by the discriminant

    4. Evaluate the discriminant to determine the number of real solutions of a quadratic equation

  • Quadratic Inequalities 2 concepts

    1. Solve inequations with a variable in the denominator and graph the solution

    2. Solve quadratic inequations and graph the solution

  • Working with Quadratic Polynomials 4 concepts

    1. Using the discriminant to determine the number of intersecting points of two graphs

    2. The identity of two quadratic expressions

    3. Equations reducible to quadratics

    4. Sum and product of roots of a quadratic function

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in The Quadratic Polynomial


  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

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Starting at

$49(inc. GST)

per session

Fully flexible

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Access to practice questions

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