ElectricPavlov

Vertex (0,0) form of this parabola 

y = d ( x-0)^2  + 0 

y = dx^2          When 2   Y = 8     So 'd' = 2 

then the equation is    Y = 2x^2        Then   A + b + c = 2 

Simplify L side 

x^2 +18x +3  = ...............      complete the square 

(x +18x + 81)  +3   - 81 

(x +9)^2 - 78           Done      

Base1 = 12 units

Base 2 = 12 + 16 = 28  units

median = (12 + 28)/2 = 20 units 

Simplify this equation to 

3y = -5x -12 

y = -5/3 x - 4        X intercept occurs when y = 0 

                                    Then x = -12/5 

                               Y intercept occurs when x = 0 

                                      Then y = -4     

• Find distance between  (-12/5 , 0 )     And   (0, -4)       Using distance formula     D = 4.66 units 

The line in y = Mx+b form is then 

       Y = 8x +14           The x-axis intercept occurs when y = 0     Put in y = o 

       0 = 8x + 14 

        X = -14/8  = - 1 3/4      <==== x intercept

ONE real root ( actually a double root) would mean the discrimination (from the Quadratic Formula) would be = 0 

b^2 - 4ac = 0        

X^2 + 4m x + m = 2x-6 

x^2 - (4m - 2) x + (m+6) = 0          A = 1      B = 4m-2     C = m+6 

(4m-2)^2 - 4 (1)(m+6) = 0 

16 m^2 -16m +4  - 4m - 24 = 0 

16 m^2 - 20m - 20 = 0          Now use quadratic formula    To find   M = 1.90587

First, find the slope between the two points:

slope     M = (y1-y2) / (x1-x2)   = (2 - -7 ) /(-8-4) =  - 9 / 12 = - 3/4 

Now the line in y = Mx + b form becomes 

                      Y = -3/4 x + b     Sub in either point to find 'b'  = -4 

then the line equation is    Y = =-3/4 x - 4     

     Re-arrange to 

          3/4 x   + y = -4       Multiply thru by 4 

            3x  + 4y = -16      Done .