Given the parabola below, find the endpoints of the latus rectum. (x-2)^2=-20(y+2)

The endpoints of the latus rectum are and .

Step-by-step explanation:

A parabola with vertex at point and whose axis of symmetry is parallel to the y-axis is defined by the following formula:

(1)

Where:

- Independent variable.

- Dependent variable.

- Distance from vertex to the focus.

, - Coordinates of the vertex.

The coordinates of the focus are represented by:

(2)

The latus rectum is a line segment parallel to the x-axis which contains the focus. If we know that , and , then the latus rectum is between the following endpoints:

By (2):

By (1):

There are two solutions:

Hence, the endpoints of the latus rectum are and .

b

step-by-step explanation:

u take $75 minus $60.the anwer/original($75)multiply by 100

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.