#### 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*) =*ax*^{2}+*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*) =*ax*^{2}+*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*) =*ax*^{2}+*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*) =*ax*^{2}+*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.