SOLUTION: Find the rule of the cubic function that passes through the points (-5,0), (2,0), (3,0) and (0,20). Give your final answer in the form y=ax^3 + bx^2 +cx +d

Algebra ->  Square-cubic-other-roots -> SOLUTION: Find the rule of the cubic function that passes through the points (-5,0), (2,0), (3,0) and (0,20). Give your final answer in the form y=ax^3 + bx^2 +cx +d      Log On


   



Question 1031408: Find the rule of the cubic function that passes through the points (-5,0), (2,0), (3,0) and (0,20). Give your final answer in the form y=ax^3 + bx^2 +cx +d
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Notice that the points (-5,0), (2,0), (3,0) give the x-intercepts of the cubic function, hence the roots of that function.
==> f%28x%29+=+k%28x%2B5%29%28x-2%29%28x-3%29+
for some undetermined constant k.
Since f(0) = 20, ==> f%280%29+=+k%280%2B5%29%280-2%29%280-3%29+=+20+ ==> k+=+2%2F3.
Therefore the function is f%28x%29+=+%282%2F3%29%28x%2B5%29%28x-2%29%28x-3%29+, which is just
f%28x%29+=+%282%2F3%29x%5E3+-+%2838%2F3%29x+%2B+20.