Algebra II: Standard Form of Quadratic Functions

Objectives

• Students will be able to predict how a specific change in the value of a will affect the shape of the graph of a quadratic f(x) = ax² + bx + c.
• Students will be able to predict how a specific change in the value of c will affect the position of the graph of a quadratic f(x) = ax² + bx + c.
• Students will be able to describe how changes in a and b will affect the coordinates of the vertex of the quadratic f(x) = ax² + bx + c resulting in both horizontal and vertical shifts.
• Students will be able to utilize the values of a and b to predict the coordinates of the vertex of the parabola and the axis of symmetry.

Vocabulary

• Compression
• Parameters
• Standard form
• Vertex

About the Lesson

This lesson involves utilizing sliders to determine the effect the parameters have upon a quadratic function in standard form.
Students will manipulate sliders and make conjectures about the relationship between:

• The value of a in the equation f(x) = ax² + bx + c and the shape of the graph.
• The value of c and the position of the graph with respect to the horizontal axis.
• The values of a and b and the coordinates of the vertex.