horizontal translation

There are two forms of the quadratic function:

y = ax^2 + bx + c

(a, b, and c are all coefficients)

OR

y = a(x - h)^2 + k   

(a, h, and k are all coefficients)

a = stretch/compression factor
h = horizontal translation
k = vertical translation

We can do the same for the cubic function:

y = (x - h)^3 + k

10 = (3 - h)^3 + 2

10 - 2 = (3 - h)^3

8 = (3 - h)^3 (take the cube root of both sides)

2 = 3 - h

h = 1

So, the function should look as follows:

y = (x - 1)^3 + 2

To check, sub in x = 3 back into the function:

y = (3 - 1)^3 + 2

y = 2^3 + 2

y = 10


Hope this helps! 

the graph of y = X3 + 2 passes through points ( 0, 2)
X needs to go up 3 units so you would subtract 3 from the X leaving you with
y= ((X-3)3) +2

now it needs to pass through 10 so the new graph equation would be:

y= ((x-3)3)+10

thanks smartie!