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A Quadratic Function Given in General and Vertex Form

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A Quadratic Function Given in General and Vertex Form

Algebra-2

Learning Made Easy

You will use appropriate strategies to convert a quadratic function from one form to the other: from vertex to general form or from general to vertex form.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Identify the vertex and general forms of a quadratic function.
  • Find the vertex of a quadratic function.
  • Identify the vertex as the minimum or maximum point on the graph of a quadratic function.
  • Write a quadratic function given in vertex form, in general form instead.
  • Write a quadratic function given in general form, in vertex form instead.

Everything You'll Have Covered

Forms of a quadratic function

The general (also referred to as standard) form of the quadratic function is f(x) = ax^2+ bx + c, where a is the leading coefficient (the coefficient of the quadratic term), b is the linear coefficient, and c is the constant term. Furthermore, if a > 0, then the parabola opens up and if a < 0, the parabola opens down.

The vertex form of the quadratic function is generally expressed as f(x) = a(x - h)^2+ k, with the value of a having the same effect on the graph of the function as it does in the general form; in addition, the values of x = h and k are the x and y-coordinates, respectively, at the vertex. For example, in the function f(x) = 2(x + 2)^2 - 2, the parabola opens up and has a minimum at the vertex (-2, -2).

Converting the quadratic function to vertex form is an integral part of graphing quadratic functions.

Converting the quadratic function from general to vertex form is an integral part of graphing quadratic functions, and Section 2 of the Activity Object provides a step-by-step procedure for accomplishing this conversion process. For example, if a student is given the following quadratic function in the general form of f(x) = ax2 + bx + c, finding the highest or lowest point (the vertex) is needed to graph the function of the parabola.

f(x) = x^2 + 4x - 3

What is clear, from the above function in general form, is that the x- and y-coordinates of the vertex are not obvious; however, a transformation (see example below) of the general form into vertex form reveals that the vertex of the parabola is (-2, -7).

Tutorial Details

Approximate Time 30 Minutes
Pre-requisite Concepts Learners should be familiar with completing the square and simplifying expressions.
Course Algebra-2
Type of Tutorial Procedural Development
Key Vocabulary completing the square, function, general form of the quadratic function