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A2.F.1.3 Graph a quadratic function. Identify the x- and y-intercepts, maximum or minimum value, axis of symmetry, and vertex using various methods and tools that may include a graphing calculator or appropriate technology.

In a Nutshell

Students will be able to graph and identify critical points in a quadratic function.

Student Actions

Teacher Actions

  • Students will be able to form conjectures and generalizations about quadratic functions, both verbally and in writing, by analyzing the graph or the equation.  

  • Students will be able to draw conjectures and make generalizations about critical points of a parabola by analyzing the characteristics of a given quadratic functions,

  • Students will understand and explain the conceptual meaning of critical points of a quadratic function and how to interpret these points in a real-world problem with the aid of technology. Students will be able to communicate their findings mathematically verbally and in writing. 


  • Provide purposeful questions that allow students to observe what causes the shape of a quadratic function in a variety of methods including using technology (Graphing calculator, desmos, etc.). Allow flexibility for students to explore other types of functions as well.

  • Implement tasks that promote discovery and reasoning on how to determine the critical points of quadratic functions. Allow multiple entry points and varied solutions strategies.

  • Engage students in graphing real world quadratic functions using a variety of methods. Pose purposeful questions for the students to identify critical points and explain the meanings in the context of the problems. Facilitate meaningful mathematical discourse by allowing time for students to share their methods with a group or whole class.

  • Use and connect mathematical representations by allowing students to explore quadratics and how they apply to real world situations this may include the use of technology.

Key Understandings


  • Identify vertex, x- and y-intercepts, maximum and minimum values.

  • Graph a quadratic function. Identify the axis of symmetry.

  • Explain how to find critical points of a quadratic function and defend the meaning of each one.

  • Identify the usefulness of critical points in a real world problem.


  • Students confuse x- and y- intercepts.  Students write x- and y- intercepts as one point.

  • Students confuse vertex with axis of symmetry.

  • Students may give axis of symmetry as a number rather than as an equation.

  • Students working with a table might pick misleading values (ie. students assume graph is linear or all critical values are integers).

  • Students have difficulty identifying the vertex.

  • Students confuse maximum/minimum value and maximum/minimum point.

OKMath Framework Introduction

Algebra 2 Grade Introduction


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