I need biiig help figuring out how to solve questions likethis: The windows are

Question

I need biiig help figuring out how to solve questions likethis:

The windows are parabolic and can be modeled by the function y=-0.575x^2 + 4.2x (x and y = feet). Graph the function. Use thegraph to determine the height and width of the window. Round to thenearest foot. The window also has a crossbar that is located 3 feetabove it's base. Use your graph to approximate the length of thecrossbar to the nearest tenth.

I honestly don't know how to do any of it even with a graphingcalculator. =/

Thanks!

Explanation / Answer

The question we need to answer then, is at what x-values doesy = 0? There will be two values, 1 at either side of thebase, and once we know the x values, the difference between them isthe width of the window.
Thus 0 = -0.575x^2+4.2x.
Factor this: 0 = x(-0.575x+4.2).
Hence, x = 0 and x = 7.304. Hence the width of thewindow is 7.304.
Now, since a parabola is symmetric, the highest point of thewindow will naturally be right in the middle. Which x valueis right in the middle? The average of the the two points wedetermined above. That is (0 + 7.304)/2 or 3.652. Plug this value of x into the equation, and find that they-value or the height of the window is 7.670.
Here's the part I will leave for you. The crossbar islocated 3 feet above the base. To determine the width, weneed to find the values of x such that -0.575x^2+4.2x = 3. This is a quadratic and we can solve for x using thequadratic formula. Then take the difference between the twovalues you get, and that is the width.
Does that help?
Cheers!

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