Question

How do you solve?

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

Answer 1

`3/4 m`

Explanation:

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