Learning Resources

Outcomes

In this lesson you will

• Use completion of the square (with aid of algebra tiles if necessary) on the general form of a quadratic function to derive its transformational form.
• Use the transformational form of a quadratic function to identify properties of the corresponding parabola, especially the location of its vertex.
• Use the transformational form of a quadratic function to solve maxima and minima problems.

By the end of this section you should be able to:

• Analyze and describe the characteristics of quadratic functions.
• Solve problems involving quadratic equations.
• Analyze scatter plots, and determine and apply the equations for curves of best fit, using appropriate technology.
• Describe and translate between graphical, tabular, written, and symbolic representations of quadratic relationships.
• Demonstrate an understanding of the relationships that exist between arithmetic operations and operations used when solving equations.
• Translate between different forms of quadratic equations.
• Describe and interpret domains and ranges using set notation.
• Demonstrate an understanding of how parameter changes affect the graphs of quadratic functions.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• The general form of a quadratic function.
• The effects of the coefficients on the shape of the graph (parabola) of a quadratic function.
• The vertex of a parabola.
• The concept of maximum and minimum values of a quadratic function.
• How to factor and expand quadratic expressions.
• How to use algebra tiles to factor and represent quadratic expressions.