Question 61942
fireworks are launched into the air. the quadratic function that models the fireworks height, s(x), in feet, x seconds after they are launched is given by the equation s(x)=-16x^2+200x+4. when should the fireworks explode so that they go off at the greatest height? What is that height?
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This is an ordinary quadratic equation so finding the vertex will give you the value of x when the maximum height is obtained.
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The vertex formula: x = -b/(2*a)
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In your equation a = -16; b = +200
:
x = -200/(2*-16)
x = -200/-32
x = +6.25 seconds after launch the firework should explode
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To find the actual height of the maximum, substitute 6.25 for x in the original equation:
s(x) = -16(6.25^2) + 200(6.25) + 4
s(x) = -16(39.0625) + 1250
s(x) = -625 + 1250
s(x) = +625 ft is the max height and occurs after 6.25 sec
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A graphical presentation would help you understand it
{{{ graph( 300, 200, -4, 16, -100, 700, -16x^2 + 200x + 4) }}}