a. y=4x^2+8x-4        answer: y = 4(x+1)²-8 
b. y=-3x^2-4x-1       answer: y = -3 + 
c. y=-5x^2+10x+1      answer: y = 5(x-1)²+6  
d. y=-2x^2+10x-11     answer: y = -2(x-5/2)²+3/2
e. y=3x^2+9x+6        answer: y = -3 - 

I'll do (b) only.  The others are the same.

 y = -3x² - 4x - 1

Factor the coefficient of x² out of the first two terms.
(Do not factor out x with it)

y = -3(x² + x) - 1

To the side multiply  by , getting 
Square  getting 

Add and then subtract  inside the parentheses:

y = -3(x² + x +  - ) - 1

Change the parentheses to brackets so parentheses may be
inserted:

y = -3[x² + x +  - ] - 1

Factor the first three terms in the brackets as a perfect
square:

y = -3[ - ] - 1

Remove the bracket by distributing the -3, remembering
to leave the  intact:

y = -3 +  - 1

Write the 1 as 

y = -3 +  - 

y = -3 + 

Now plot the vertex (,)



Find the x-intercepts by setting y = 0

              y = -3x² - 4x - 1 

              0 = -3x² - 4x - 1

   3x² + 4x + 1 = 0

(3x + 1)(x + 1) = 0

3x + 1 = 0                x + 1 = 0
    3x = -1                   x = -1
     x = 
    
So the x intercepts are (,0) and (-1,0)
Plot them.


           
Find the y-intercept by letting x = 0 in the original

 y = -3x² - 4x - 1
 y = -3(0)² -4(0) - 1
 y = 0 - 4 - 1
 y = -1

So plot the y-intercept (0.-1) too



Now draw a smooth parabola through those 4 points:




Edwin