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Real life Quadratics
Plus Relative Maximums, Minimums and
Zero’s
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Warm Up:
Evaluate for f(9) and f(2)
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Objective
The student will be able to identify relative maximums and minimums, and zero’s of functions.
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Explore
Non-linear functions explore worksheet.
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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.
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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.
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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.
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Maximums and Minimums
Maximum Minimum
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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.
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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.
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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.
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Exit Ticket
Exit Ticket: Determine the Zero’s and either relative max or min.