Baseball Parabola Handout

Parabolas in Real Life (baseball) All units are in feet

150

c b

100

50

( ( 0

,

50

,

( )

,

)

(

a ,

) fence

) 100

150

200

250

300

350

Please note that f(x) is basically another way of saying y.

200 250 300 350 formula: f(x) =

f(x)

x predicted data observed data

x

b

}{ }{

200 250 300 350

formula: f(x) =

c

f(x)

x predicted data observed data

a

}{ }{

200 250 300 350

formula: f(x) =

f(x)

There is a 10-foot tall fence at 370 ft from the batter. The question for each of the three balls that were hit is, “will it be a home run?” For each one, find f(370) and use that information to find whether the ball clears the fence (if it is greater than 10, then it clears the fence!). To find f(370), just substitute 370 into the equation to find the height—y or f(x)—when the ball is 370 feet from home plate. Ball a:

Ball b:

Ball c:

A property of parabolas is that the x-coordinate of the vertex can be found by −b −b . . The y-coordinate is found by calculating f  2a 2a −b −b Basically this means that the vertex is at the point ,f  . 2a 2a calculating





Calculate the vertex for each of the three balls and label the vertex on the other side. Ball a:

Ball b:

Ball c:

Finally, try to draw the whole path of each hit using the predicted values and the vertex.