Question 1177173: https://gyazo.com/fe86195bd0e154bae1ff5d3272b3ef30
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Determine the equation of a cubic with inflection point at (-1,-2) and passing through the points (-3,-8) and (1,4).
Note: We only need to use one of the points (-3,-8) and (1,4) in our calculations. (-3,-8) is 2 units left and 6 units below the inflection point, and (1,4) is 2 units right and 6 units above the inflection point. Since the graph is symmetric with respect to the inflection point, we know both of those points will be on the graph.
The basic cubic is  , which has inflection point at (0,0). This graph has inflection point at (-1,-2), so it has been shifted left 1 and down 2. We don't yet know if the function has been stretched vertically or horizontally, so the function at this point is
 [1]
I much prefer determining the stretch factor informally, like this:
2 units to the right of the inflection point, the function value for y=x^3 should have increased by 2^3=8. On this graph, 2 units to the right of the inflection point the value has only increased by 6. So the stretch factor is 6/8 = 3/4.
So the function in the graph is
If you want or need to find the stretch factor formally, plug the point (1,4) into equation [1] and solve for a:
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