Please help me!

1. The speed giving the best fuel economy wiil be the x coordinate of the vertex of this parabola

So  we have  y  = -.0075x^2 +.575x + 11.5

The x coordinate of the vertex  in the form  y  = ax^2  + bx  + cc is given by   -b/ [ 2a]

So.....plugging in what we have leads to :     -.575 / (2 * -.0075)   ≈ 38.33  ≈  38 mph 

2.  -3x^2 +2x  -3  = 0      we can us the quadratic formula to  find the solutions

x  =  (  -2 ±√ [ 2^2  - 4(-3)(-3)  ]  )  / 2 (-3)  =

=   (-2 ±√ [4 - 36 ] ) / -6  =

( -2 ±√ [ -32 ] )  /-6

(-2 ± i√  [ 16 * 2 ] )  /-6  =

( -2 ±  4i√2   ) / -6      =

( -1 ± 2i√ 2) / -3   ⇒    "C"

3.  (5x  -15)^2  = -100       take both roots

5x  - 15  = ±√(-100)

5 ( x - 3)  = ± i √ 100

5 ( x - 3)  = ±10i      divide through by 5

x  - 3   =  ±2i       add 3 to both sides

x =  3 ± 2i    ⇒   "C"    

Thank you so much for your help!! I appreciate it!