Ireally am bad with math and just have given up
with trying to solve these equations can someone

Well hmmm does the graph open upwards or downwards?  well
is a quadratic, if the leading term's coefficient is negative, Down, if positive, Up

a)
now, let's see the leading term, -x², what's its coefficient? is -1 * x² or -1x², is -1, so is negative, thus is opening downwards

c)
x-intercepts occur, when y = 0, namely y = -x²-4x-3, so setting y to 0
0 = -x² -4x -3 take a common factor of -1, thus

0 = -1 (x²+4x+3)  <--- now, if we factor that out, notice, surely you've done many of these by now, so we end up with 



so, the x-intercepts are at -3 and -1

d)

now, the y-intercepts, just set x = 0
y = -x²-4x-3, settting x to 0 y = -0²-4(0)-3, which is y = -3

so the sole y-intercept is at y = -3

now, let's get on to b)

b)   

and those are the coordinates, notice a = -1, b = -4 and c = -3

now, for

e)

well, all you have to do is, once you have the vertex, pick an x-value on the left-hand-side of the vertex, get they value for "y", or OUTPUT,

then pick another x-value, on the right-hand-side of the vertex, get the "y" value again, and plot away

The answer is 10. and if you go by pemdas you would 1. multiplication 2. division 3. addition 4. subtraction