Question 77574: can someone please help me with this. What is the particular equation for the quadratic function described in the situation.
The sluggers were up to bat in the bottom of the ninth inning in a game against the ditchers. Theo Slam was up to bat. As he plugged the ball toward left field, it rose from 3 to 10 to 50 feet as the horizontal distance from home plate increased from 0 to 2 to 14 feet. Assume that the vertical distance varies quadratically with the horizontal distance.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! As he plugged the ball toward left field, it rose from 3 to 10 to 50 feet as the horizontal distance from home plate increased from 0 to 2 to 14 feet. Assume that the vertical distance varies quadratically with the horizontal distance.
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You have three tracking points: (0,3),(2,10),(14,50)
The equation is y=ax^2+bx+c
Substitute the point values and solve for a,b,c
3=0a+0b+c
10=4a+2b+c
50=196a+14b+c
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Solve the system of linear equations.
I used a TI calculator's matrix method to get:
X=A^-1B
a= -0.0119047
b= 3.5238095
c= 3
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EQUATION:
y=-0.119047x^2+3.5238095x+3
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Cheers,
Stan H.
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