Can anybody help me with trying to figure out how to do this?

a. Angle A  = 35

As triangle ABD has angle ADB equal to 90°

=> ABD is the right triangle

=> Angle ABD + Angel A = 90°

=> Angel A = 90° - Angel ABD = 90°- 55° = 35°

So Angel A = 35°

b. Angle CBD = 61

As triangle BDC has angle BDC equal to 90°

=> BDC is the right triangle

=> Angle CBD + Angel C = 90°

=> Angel CBD = 90° - Angel C = 90°- 29° = 61°

So Angel CBD = 61°

c. AD = 32.77

As ABD is the right triangle, so that we have the formula:

sin (an angel) = opposite side/ hypotenuse

=> sin angel ABD = AD/ AB

=> AD = sin angel ABD x AB = sin 55° x 40 ≈ 32.77

So AD = 32.77

d. BC = 47.32

As ABD is the right triangle, according to Pythagoras theorem, we have:

=> BD ≈ 22.94

As BCD is the right triangle, so that we have the formula:

sin (an angel) = opposite side/ hypotenuse

=> sin angel C = BD/ BC

=> BC = BD/ sin angel C = 22.94 / sin 29° ≈ 47.32

So BC = 47.32

e.  CD = 41.39

As BCD is the right triangle, according to Pythagoras theorem, we have:

=> CD ≈ 41.39

f. BD = 22. 94 (part d)

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.