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A ball is thrown into the air. The height of the ball can be modeled by the equation y = 5 + 30x - 4x^2What do the numbers 5, 30 and -4 mean in this situation?

User Sir Visto
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We have the following quadratic function:


y=-4x^2+30x+5

Since a quadratic function represents a parabolla, we have a different meaning for each coefficient. In this case, we have the following:


a=-4<0

first, we have that the main coefficient is -4, which is less than 0. Thus, the parabola will be wider. In the context of this problem, this means that the ball will take more time to touch the ground.


b=30

the second coefficient determines, along with the coefficient 'a', to which side the parabolla will move with respect of the y-axis. In this case, since a<0 and b>0, we have that the parabolla will move to the right of the y-axis. Which is clear, since we are measuring with only positive values of the time.


c=5

finally, the last coefficient is 5, which represents a constant and the y-intercept of the parabolla. Therefore, in this case it represents the initial height of the ball

User Nick Butler
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