ElectricPavlov

Using the formula that Melody posted....  I get   Karlee has ( r = .006666667    I think this is where our answers differ)   894,064.89

    and Chase has  702 856.24

Start with vertex form of a parabola

y = a (x+2)^2 -1        sub in point   0,6    to find a = 7/4

y = 7/4 (x+2)^2 -1

I do not know the units   but   ( 9.4 x 10⁸ )  / ( 8.760 x 10³) = ....................  units/hr

Just put '1' in for 'x' and calculate 'b'

3 (1⁴) - 7 (1³) - 2(1²)  - b (1) + 1     =  1      solve for 'b'

ax^2 + 20x + 7 = 14x + 9             re-arrange

ax^2 + 6x -2 = 0          for only one solution ( one double root) the discriminant of the Quadratic Formula must = 0

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

b^2 - 4ac = 0

(6)^2 - 4 (a)(-2) = 0

8a = -36

a = -4.5

Probably easiest to use Quadratic Formula

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)      a = -.015          b = 1.875          c = 1.59375

y = ( x - 125.844)(x + .844297)  

Try  (0,0)     

x^2+y^2-6x+4y+4=0       put into standard circle equation form

x^2 - 6x      +    y^2 + 4      = - 4       now, complete the square for x and y

(x-3)^2       +   ( y+2)^2     = - 4  + 9 + 4

(x-3)²         + ( y+2)²       = 9                     center is thus seen as   3, -2     and radius = sqrt 9 = 3

(2x -1 )(x  +3 ) = 0     shows x = 1/2  and  -3