Purpose

To relate quadratics, their solutions, and properties both graphically and algebraically.

Objectives

The student will be able to graph a quadratic function.

The student will be able to determine the effect of 'a' of y =ax^2 for a>1.

to determine the direction of the graph, the vertex point

and whether the vertex point is a **maximthe
student will be ableum** or **minimum**
point.

The student will be able to determine the axis of symmetry, and thex-intercepts of the graph of

the function.

The student will be able to determine the domain and the range of the quadratic function.

The student will be able tosolve quadratic equations by using the quadratic formula.

The student will be able to use the discriminant to determine the nature of the solutions of a

quadratic equation.

The student will be able to determine the relationship between the nature of the solutions and

the graph of a quadratic function.

Overview of content

This unit is about Quadratic Functions. Quadratic functions will be investigated graphically and algebraically. The components of the equation which defines the quadratic function will be identified as predictors of how the graph will look. Observations of the graph such as vertex, axis of symmetry, direction of the graph will be noted also. Parameter investigation of "a" in the y = ax , shall be done to explore the stretching or shrinking effect of the graph. A parameter investigation of 'k' in the equation y = x + k will the done also. Application of the quadratic formula to solve quadratic equations will be studied. Identifying the solution(s) to the quadratic from the graph (x-intercepts) shall be handled. Lastly, finding the discriminant and using it to determine the nature of the solutions of the quadratic equation as well as determining the relationship between the nature of the solutions and the graph of the quadratic function will be covered.

Materials needed

Textbook, paper, graph paper, pencil, colored highlighters, TI-82 OF TI-83

Time

5 - 8 CLASS sessions

**TEKs**

**Prior
knowledge**

The student will need prerequisites of graphing order pairs, evaluating expressions, reading x/y table of values, using TI-82 OR TI-83 GRAPHING CALCULATOR.