The polynomial of degree 3 , P(x) , has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=-4 . The y -intercept is y=-12.8 .
Find a formula for P(x)
what I have tried.. -12.8=a(x-4)^2(x+4)
I get confused and start adding steps I shouldn't.
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You were on the right track with
a(x-4)^2(x+4),
but leave P(x) equal to that:
P(x) = a(x-4)^2(x+4)
Now use this given fact:
The y -intercept is y=−12.8
Think about what y-intercept means. Remember that y = P(x). The y-intercept
being -12.8 means that when you substitute x=0, you get y = P(0) = -12.8
So substitute x=0 in
P(x) = a(x-4)^2(x+4)
P(0) = a(0-4)^2(0+4)
12.8 = a(-4)^2(4)
12.8 = a(16)(4)
12.8 = a(64)
= a
0.2 = a
Now substitute 0.2 for a in
P(x) = a(x-4)^2(x+4)
Answer:
P(x) = 0.2(x-4)^2(x+4)
That's the answer. Or you can multiply it out:
P(x) = 0.2x^3-0.8x^2-3.2x+12.8
Edwin