Real life Quadratics

Plus Relative Maximums, Minimums and

Zero’s

Warm Up:

Evaluate for f(9) and f(2)

Objective

The student will be able to identify relative maximums and minimums, and zero’s of functions.

Explore

Non-linear functions explore worksheet.

Try with a Partner:

Fireworks go off at their highest point and can be represented by the following equation:

Graph the equation and determine the time t in which the firework is at it’s maximum height and find the height in meters.

Quadratic Function

A quadratic function is written in the form:

y = ax2+bx+c where a does not equal 0.

Note: this is called standard form.

The equation forms a parabola when graphed.

Parabolas

Parabolas have either a maximum or a minimum.

Maximum: The highest point on the graph.

Minimum: The lowest point on the graph.

Parabolas also have zeros, which are where the the parabola crosses the x-axis.

Maximums and Minimums

Maximum Minimum

Try with a Partner:

Jumping into a pool off a diving board 2.5 feet from the surface of the water can be represented by the following equation:

Graph the equation and determine the time t when you are at the deepest point and find how deep you go in feet.

On your Own:

Shooting off a rocket can be represented by the following equation:

Determine how many seconds the rocket was in the air.

Determine the maximum height of the rocket.

On your Own:

Punting a football can be represented by the following equation:

Graphically represent the equation and find the hang time of the football.

Determine the maximum height of the football.

Exit Ticket

Exit Ticket: Determine the Zero’s and either relative max or min.