Question

Can someone help me with this question please?

Answer 1

The results of the analysis are:

a) The quadratic function that represents the dam arch is
`y - 4 = (1)/(6) \cdot (x - 50)^2`.

b) The inequality that represents the region below the parabolic arch is
`y < (1)/(6)\cdot (x - 50)^2+4`.

How to apply and analyze a quadratic equation in a dam arch

In this problem we must use and understand quadratic equations to analyze the arch of a bridge. Quadratic equations can be represented by vertex form:

y - k = C · (x - h)²

Where:

• h, k - Vertex coordinates.
• C - Vertex constant.

a) If we know that (h, k) = (50, 4) and (x, y) = (0, 0), then the equation of the dam arch is:

`C = (y - k)/((x - h)^2)`

`C = (0 - 4)/((0 - 50)^2)`

`C = (1)/(625)`

`y - 4 = (1)/(6) \cdot (x - 50)^2`

b) The inequality that approximates the region below the parabolic arch of the dam is:

`y < (1)/(6)\cdot (x - 50)^2+4`