Lesson 2 Flipping Ferraris Solidify Understanding

Ready

Solve for .

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Students were given a set of data to graph. After they had completed their graphs, all students shared their graphs with their partners. When Ethan and Emma saw each other’s graphs, they exclaimed together, “Your graph is wrong!” Neither graph is wrong. Explain what Ethan and Emma have done with their data.

Ethan’s graph:

A coordinate grid with points at about (0.1,0.2), (1,1), (2.1,1.5), (4,2), and (6.2,2.25) x222444666y222444666000

Emma’s graph:

A coordinate grid with points at about (0.2, 0.1), (1,1), (1.5,2.1), (2,4), and (2.25, 6.2) x222444666y222444666000

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Describe a sequence of transformations that would take Ethan’s graph onto Emma’s graph.

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A baseball is hit upward from a height of with an initial velocity of (about ). The graph shows the height of the ball at any given second during its flight.

Use the graph to answer the following questions.

A quadratic graph modeling the height of a baseball hit over time. 22244466620202040404060606080808010010010000099 ft67 ft3 fttime in secondsheight in feet

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Approximate the time that the ball is at its maximum height.

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Approximate the time that the ball hits the ground.

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At what time is the ball above the ground?

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Make a new graph that shows the time when the ball is at the given heights.

A blank coordinate plane with the x axis labeled as height in feet and the y axis labeled as time in seconds height in feettime in seconds

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The new graph is the inverse of the time vs height graph, but it is not a function. How would you restrict the domain on the original function to make it invertible?

Go

The functions are defined:

Calculate the indicated function values.

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Notice that the notation is indicating that you replace in with .

Find the following using substitution.

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