Unit 8 Lesson 6: Introduction to Quadratic Functions

Objective: Identify a quadratic function and the values of the coefficients and constant from the standard form, evaluate a quadratic function given different representations, and calculate the rate of change of a quadratic function over an interval.

Analyzing Projectile Motion

Juan is studying medieval catapults that were used to project castles. He recorded a reenactment and plotted the path of the projectile at different heights each second after launch.

The table and graph show symmetry on both sides of the maximum point.

Defining Quadratic Functions

· Projectile motion is modeled using a _________________________ function.

· A quadratic function is a second degree polynomial of the form:

Identifying Values of Quadratic Functions

Identify the values of a, b, and c for the quadratic function .

a = b = c =

Graphs of Quadratic Functions

The graph of a quadratic function is called a _________________________.

If a > 0, the parabola opens ____________. If a < 0, the parabola opens ____________.

The parabola shown is the graph of the quadratic function

a = _____b = ____c = _____

Domain: {x|x is a ____________ number}

Range: {y| y __________}

Comparing Functions

· Compare the ______________________________ of and .

· Compare the rate of change of and

Evaluating Quadratic Functions

Example: Evaluate the function for an input of 1.

Example: Evaluate the function for an input of -3

Example: Evaluate the function for the input values -2, 0, and 3.