On page 162, in the first word problem, the professor says that Pal can only catch the ball when it is exactly 10 units about the ground. I wonder why does it have to be exactly 10 units? What if he bent down to get the ball, or if he jumped up? When I've seen baseball games, the outfielder uses different strategies to try to catch the ball at different heights, so I wonder why Pal can only catch the ball at exactly 10 units.
When the king described the function for the ball, that x is the time since the ball left the bat, and y is the height of the ball above the ground, I could already see a graph forming in my mind. I could see an imaginary line measuring time going from the bat to the outfield, I could see another imaginary line from the group up towards the ball, measuring its height.
On the next page , they explain that after hitting a lot of fly balls, they came up with the equation f(x) = -x^2 + 7x. I don't understand how the data was transferred into this function. I re-read the passage a few times and I still feel like there was a step skipped.
The professor then said that f (x) = 10. I'm confused why this is, but I guess you just have to trust him.
After plugging that in we got that x^2 - 7x +10 = 0.
After finding this equation, we could use it to make a graph. I could see the lines of the graph, with the x and y axis. After having an image in my head, I thought that if we plug in numbers for x, we will get the y coordinates, and then we can graph the equation. Looking at the graph I was confused to what the curve meant, at what point could Pal catch it? What did all these numbers mean?
I re-read the entire problem. I realized that when f (x) = 10, that was where Pal could catch it, so we were trying to figure out the time. After plugging in numbers, we found that there were 2 different points on the graph that solved the equation. I couldn't figure out which was the right one, even after re-reading the problem and looking at the graph. I double checked my numbers and they still worked.
I think that was enough math for one night, so I'm going to put it aside and hopefully return refreshed another time.
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well written and very informative. I have been there, when I've felt like I've had enough math...lol. I love how hard you worked at trying to relay the text in a way that everyone can understand. you def need patience to do that.
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