Intro Question: Checkerboard
Concepts Covered:
Answering Questions about Quadratics
Homework Problems; what do the graphs from each problem tell us? What are the points we care about?
Where it crosses the x-axis
Where the peak is
What is the graph actually representing?
height compared to time.
Farmer John Rears his head again --> building a model
Maximum area for a rectangular object
Maximum of the object on the river
How do we graph Quadratics (what are the forms that matter?)
Vertex form is created when we know the height of an object.
Intercept form is fantastic when we know where the object crosses the x-intercept
Standard form is good when given to us, can help us solve problems
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make a model of falling objects. try to create an equation with that data
calculate height and time of a falling ball
graph these things
try to find an equation to go with it (obviously it's not linear--or at least it best not be)
make an equation dealing with the falling wrench
He dropped a wrench from the 30th floor?!
http://www.ctbuh.org/TallBuildings/HeightStatistics/HeightCalculator/tabid/1007/language/en-US/Default.aspx
what is the height at which we would be "Safe"?
(this should create a more general equation for us)
make an equation dealing with the power plant
8 miles downstream. river is 3/4 of a mile wide
how do we generalize?
make an equation dealing with the car