Question 1169290
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Graph your concave down parabola with the vertex at the origin.  Since it is 3 m high, the bottom must be at -3, and since it is 8 meters wide centered on the vertical axis, it must extend from -4 to 4 at the bottom.  That gives us three points, sufficient to define a parabola.  Putting the vertex at the origin eliminates the constant and first degree terms, simplifying the function considerably.


The points are *[tex \Large (0,0)], *[tex \Large (4,-3)], and *[tex \Large (-4,-3)], so if any parabola with a vertical axis can be modeled by *[tex \Large y\ =\ ax^2\ +\ bx\ +\ c], we know that, for this parabola:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0a\ +\ 0b\ +\ c\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 16a\ +\ 4b\ +\ c\ =\ -3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 16a\ -\ 4b\ +\ c\ =\ -3]


Solve the 3X3 system for the coefficients of the desired function. Hint: *[tex \Large b] and *[tex \Large c] will both be zero as a consequence of placing the vertex at the origin.


Once you have the desired function, calculate the value of the function at one-half the width of the truck, then subtract this value from 3 meters to find the maximum height of the truck.

																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
*[illustration darwinfish.jpg]

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