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Algebra 1

7.14.3 Analyzing Functions Using Different Representations

Algebra 17.14.3 Analyzing Functions Using Different Representations

7.14.3 Analyzing Functions Using Different Representations

7.14.3 • Analyzing Functions Using Different Representations

Activity

Here is a graph that represents the height of a baseball, h h , in feet as a function of time, t t , in seconds after it was hit by Player A.

The function g g defined by g ( t ) = ( − 16 t − 1 ) ( t − 4 ) g ( t ) = ( − 16 t − 1 ) ( t − 4 ) also represents the height in feet of a baseball t t seconds after it was hit by Player B. Without graphing function g g , answer the following questions and explain or show how you know.

1.

Which player's baseball stayed in flight longer?

2.

Which player's baseball reached a greater maximum height?

3.

Based on the graph, what is the approximate height, in feet, of Player A’s baseball when hit? How do you know?

4.

What is the height, in feet, of Player B’s baseball when hit?

Video: Comparing Quadratic Functions

Watch the following video to learn more about comparing quadratic functions in different forms.

Comparing Quadratic Functions

Self Check

The functions describing the time that baseballs stayed in the air, in seconds, that four baseball players hit are below.

  • f ( t ) = ( − 16 t − 1 ) ( t − 5 )
  • g ( t ) = ( − 16 t − 1 ) ( t − 10 )
  • h ( t ) = ( t − 7 ) ( − 16 t − 1 )
  • p ( t ) = ( − 8 t − 1 ) ( 2 t − 5 )

Which function represents the ball that stayed in the air the longest?

  1. p ( t ) = ( − 8 t − 1 ) ( 2 t − 5 )
  2. h ( t ) = ( t − 7 ) ( − 16 t − 1 )
  3. g ( t ) = ( − 16 t − 1 ) ( t − 10 )
  4. f ( t ) = ( − 16 t − 1 ) ( t − 5 )

Additional Resources

Comparing the Graphs and Equations of Quadratic Functions

Jai kicks a football. The graph that represents the height of the football, h h , as a function of time, in seconds, is below.

Kellan kicks a football and the height in feet, h h , is represented by the function h ( t ) = ( − 16 t − 1 ) ( t − 6 ) h ( t ) = ( − 16 t − 1 ) ( t − 6 ) .

Which player’s football stayed in the air longer?

Jai’s football landed after 4 seconds since the zero is at x = 4 x = 4 . The other zero, where x x is negative, does not make sense in this problem.

Looking at the function of Kellan’s ball, find the zeros by setting each factor equal to zero.

  • − 16 t − 1 = 0 − 16 t − 1 = 0 becomes t = − 1 16 t = − 1 16 . A negative time does not make sense in this problem.
  • t − 6 = 0 t − 6 = 0 becomes t = 6 t = 6 .

Kellan’s ball was in the air for 6 seconds, so his ball stayed in the air 2 seconds longer than Jai’s.

Try it

Comparing the Graphs and Equations of Quadratic Functions

Using the same information above, which player’s football reached a higher height?

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