Question

MODELING REAL LIFE A baseball is thrown up in the air. The table shows the heights $y$ (in feet) of the baseball after $x$ seconds.Time, x0.511.52Baseball height, y18242212Write an equation for the path of the baseball.Equation:Find the height of the baseball after $1.7$ seconds.Height:ft

Answer 1

The equation for the path of the ball can be measured using a regression model calculator which produced the quadratic model ;

• y(x) = - 16x² + 36x + 4
• Height at x = 1.7 = 18.89 feets

The table given :

Time, x : __0.5 ___ 1 ____ 1.5 ____ 2

Height, y _ 18 ____22 ___ 24 ____ 12

Using technology such as a quadratic regression calculator or excel ;

The quadratic regression model obtained is :

• y(x) = - 16x² + 36x + 4

The height after, 1.7 seconds, x = 1.7 can be calculated thus :

Put x = 1.7 in the equation :

• y(1.7) = - 16(1.7)² + 36(1.7) + 4
• y = 18.89 feets

Therefore, the height of the baseball after 1.7 seconds will be 18.89 feets.

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