let f(x)= a(7-x^2) for everywhere a doesn't equal x

A) find, in terms of a, the equations of the lines tangent to these curves at x=-1.

so i took the derivative of the function and got f'(x)=-2ax and f'(1)=2a

i then plugged -1 into the original equation and got f(-1)=6a. so i used point slope formula and slope intercept to get the function of the tangent line to be y=2ax+8a

Very well done..though you meant
B) find, in terms of a, the y intercepts of the tangent lines at x=-1

i found the y int by letting x=0 and solving for y

so i had y=2a(0)+8a and got y int=8a

C) find the x intercept of the tangent lines at x=-1

i did this by letting y equal o and solving for x

so i had 0=2ax+8a and got x int=-48

Why?? , unless , but then the function is zero and all the rest is zero, too
I triend checking this on my calculator by putting in a constant for a, i think i'm good with a and b but unsure if my c came out correctly

also, the questions say the y intercepts of the tangent lines, however I only got one tangent line at x=-1, am i right or wrong about this?