Question

The image of a parabolic mirror is sketched on a graph. The image can be represented using the function y = 1/8x2 + 2, where x represents the horizontal distance from the maximum depth of the mirror and y represents the depth of the mirror as measured from the x-axis. How far away from the maximum depth is a point on the mirror that is 7/8 inches in depth?

3 inches
4 inches
5 inches
6 inch

Answer 1

three inches deep#!!!

Answer 2

3 inches depth

Explanation:

Given the equation of the parabola is

y =
`(1)/(8)* x^(2)+2`

where x represents the horizontal distance from the maximum depth and y represents the depth of the mirror as measured from the x axis.

We need to find the distance from the center of the parabola which is 7/8 inches in depth from the mirror. Therefore substituting the value of x as 7/8 inches in the above equation, we can get the value of y.

∴y =
`(1)/(8)* \left ( (7)/(8) \right )^(2)+2`

y =
`(1)/(8)* \left ( (49)/(64) \right )+2`

y = 0.09+2

y = 2.09

y = 3 inches (approx )