I have a math question showing a cubic function on a graph but there aren't 3 x-intercepts points to use to find the equation of the graph there is only one point where the function passes through at x=0 and then there is an inflection point at (2, 2.7) and then the function continues to increase. So whats the formula to figure out the equation in this case? Thanks!
Find equation for cubic graph?
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Steven G
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Are you saying that this cubic has no x-intercepts? So it goes from -infinity to positive infinity without crossing the x-axis? This is not possible. Or does it have some x intercepts but you do not know them?
You say that the function passes through a point where x = 0. Can you please give us the y value at this point.
It would be best if we can have a picture of this function.
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Assuming you meant the value of y (the cubic equation) was zero when you said "...there is only one point where the function passes through at x=0 ...", we have a point (0,0) on the curve and a point of inflection at (2,2.7). First the point of inflection: At a point of inflection (x0, y0), the first and second derivative is zero and (for a cubic) the third derivative is not zero. The latter just says the coefficient of x3 isn't zero. If f is a cubic, f' is a quadratic, and f'' is linear. Since f'' is zero at x=x0,
f''(x) = 6 a(x-x0)
for some constant a and, integrating and using f'(x0) = 0,
f'(x) = 3 a (x-x0)2
Thus, integrating and using f(0) = 0, we have
f(x) = a (x-x0)3 + a x03 = a [ (x-x0)3 + x03 ]
Now, since the point of inflection is at (2, 2.7), x0 = 2 and f(x0) = 2.7 or
a x03 = 2.7
or
a = 2.7/8
Thus the function is
f(x) = 2.7 [ (x - 2)3 + 1]
If you wanted to play around it could be reformulated.
EDIT: Fix dumb mistake
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