In a real-life situation, to model the distance x and the height of hitting a baseball y as in: y = ax^2 + bx + c
1. When dealing with the initial height of the ball, what is happening when x = 0?
Is it that the ball has not yet traveled any distance?
2. What are the possible values for y when x = 0?
I know only the constant term would be left. So would I be correct in saying "the constant term" or how do I better say it?
3. Regarding the maximum height of the ball: knowing some values of y are not reasonable, how does that affect choosing a window for the graph?
When x = 0, the ball is leaving the bat
y then is c, the initial height. That is the only possible value for y
As far as question 3, I would choose a horizontal range domain maybe ten times as long as the max height I expected.
1. When x = 0 in the equation y = ax^2 + bx + c, it represents the initial condition or starting point of the ball's trajectory. In a real-life scenario, x = 0 corresponds to the moment when the ball is hit or thrown. At this point, the ball has not yet traveled any distance, so it has no horizontal displacement.
2. When x = 0, plugging it into the equation y = ax^2 + bx + c results in y = c. The constant term, represented by 'c' in the equation, gives the initial height of the ball. It represents the vertical position of the ball at the time of release or impact. So, you can correctly say that when x = 0, the possible value for y is "the constant term" or "the initial height of the ball."
3. In the context of modeling the maximum height of the ball, it is important to consider physical constraints to avoid unreasonable values. For example, negative values for y or values that exceed practical limits would be unreasonable. When choosing a window for the graph, you should set the range of the y-axis to accommodate reasonable values based on the specific scenario. By doing so, you can exclude unrealistic or physically impossible results from the graph and focus on visualizing the relevant and meaningful data.