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Liula [17]
3 years ago
5

find the equation of a cubic function whose graph passes through points (3,0) and (1,4) and is tangent to x-axis at the origin

Mathematics
1 answer:
Tomtit [17]3 years ago
3 0

Answer:

y = -2x^2(x - 3)

Step-by-step explanation:

<em><u>Preliminary Remark</u></em>

If a cubic is tangent to the x axis at 0,0

Then the equation must be related to y = a*x^2(x - h)

<em><u>(3,0)</u></em>

If the cubic goes through the point (3,0), then the equation will become

0 = a*3^2(3 - h)

0 = 9a (3 - h)

0 = 27a - 9ah

from which h = 3

<em><u>From the second point, we get</u></em>

4 = ax^2(x - 3)

4 = a(1)^2(1 - 3)

4 = a(-2)

a = 4 / - 2

a = -2

<em><u>Answer</u></em>

y = -2x^2(x - 3)

 

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