Question 720575: Not Urgent, Just VERY Curious
Hello, I couldn't find the correct section for my question. I am having difficulty with a certian concept in my math 170 class. We were recently taught about building functions, and specifically how to express the area of a rectangle as a function of x. In the example we are shown that a rectangle with its corners on origin, positive x, positive y, and a point in quadrant I on the graph y = 25 -x^2. I get all that, I can crunch the numbers, and come up with the right answers, but I have no idea what this function represents. It later says that the maximum area is 48.11 square units at x=2.89 units. What is x representing here? What is this area related to? How does this information corrospond to a practical application of mathematics? I am very sorry if I'm wasting your time, but I am on the verge of chewing my own fingernails off. I have to know what this actualy means. I've tried using the internet, and I keep getting function problems, not explainations. Thank you for your time, and have a wonderful day.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! y = 25 -x^2
I will give it a try:
The given equation is that of a parabola that open downward (curve has a maximum).
Its standard form: y=A(x-h)^+k, (h,k)=(x,y) coordinates of the vertex.
For given equation: y=25-x^2
rewrite: y=-x^2+25
Since you don't see h, the x-coordinate of the vertex is=0
The y-coordinate of the vertex is=k=25 which is also the maximum value for that particular parabolic function. A which is assumed=1, affects the slope of steepness of the curve.
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As for the maximum area is 48.11 square units at x=2.89 units, this must represent a different curve from the one above. If it is a parabola it would be like: y=-(x-2.89)^2+48.11, that is, coordinates of the vertex would be (2.89,48.11)
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In math and physics applications of the parabola is quite common especially in higher math courses like calculus. To get a better understanding of what the different curves look like, get a graphics calculator and punch in the equation to display the curve.
Hope this helps!
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