Answer to Question #72769 in Algebra for Jimmy Smith

Question

Suppose that by midnight the vertex of the front has moved 250 miles south and 210 miles east of Des Moines,
maintaining the same shape. Write the equation for the parabola that would represent the cold front at midnight.
(Remember: both longitudinal and latitudinal distances are measured in hundreds of miles.)

Answer 1

South is negative y direction (down).
North is positive y direction (up).
East is to the right, positive x.
West is to the left, negative x.
Each unit represents 100 miles.
We have the function with Des Moines at (0,0)
f_1 (x)=1/20 x^2
When the vertex of the front has moved 250 miles south, then the function will be:
f_2 (x)=1/20 x^2-250/100
f_2 (x)=1/20 x^2-2.5
And 210 miles east:
f_3 (x)=1/20 (x-210/100)^2-2.5
f_3 (x)=1/20 (x-2.1)^2-2.5
Therefore, the equation for the parabola that would represent the cold front at midnight is
f(x)=1/20 (x-2.1)^2-2.5
Simplify
1/20 (x-2.1)^2-2.5=0.05(x^2-4.2x+4.41)-2.5=
=0.05x^2-0.21x-2.2795
Answer: f(x)=1/20 (x-2.1)^2-2.5 or f(x)=0.05x^2-0.21x-2.2795 .