Tracking the height of a Baseball
The graph of the equation
h = -at
+ bt + c
which describes how the height, h, of a hit baseball changes over time, t, is show below.
If you alter only this equation’s c term, which gives the height at time t = 0, the alteration has an effect on which of the following?
- The h-intercept
- The maximum value of h
- The t-intercept
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1 solution
The equation we are given h = -at 2 +bt + c is a parabola and we are told to describe what happens when we change c (the y-intercept).
From what we know about functions and function translations, we know that changing the value of c will shift the entire parabola upwards or downwards, which will change not only the y-intercept (in this case called the “h intercept”), but also the maximum height of the parabola as well as its x-intercept (in this case called the t intercept). You can see this in action when we raise the value of the y-intercept of our parabola.
Options 1, 2, and 3 are all correct.