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Question

A parabolic solar cooker is manufactured following the equation y = 4x^2 - 4X + 1/4, and is mounted on a tabletop whose edge coincides with the axis of the abscissa. If all measurements are given in meters, determine the depth of the counter so that the kitchen fits perfectly.

A)1/2 - (√3/4)
B) 1/2
C) 1/2+(√3/4)
D)3/4

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Answer 1 · 2018-01-24T22:46:22

#3/4 m#

graph{4x^2-4x+ 1/4 [-10, 10, -5, 5]}

this is the parabola of #y = 4x^2-4x + 1/4#.

depth of counter: vertical distance from tabletop to bottom of cooker

depth of counter: vertical (#y-#) distance from the abscissa to the vertex of the parabola

coordinates of vertex: #(0.5, -0.75)#

at the abscissa, #y=0#
at the vertex, #y=-0.75#

depth #= 0 - (-0.75) #

#= 0 + 0.75 #

#= 0.75#

#0.75 = 3/4#

depth of counter: #3/4#m