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The curve above is the graph of a degree 3 polynomial. It goes through the point (5,−6.3). what is the polynomial please? image attached

Mathematics
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1 Attachment
a sum of several terms produces a polynomial
i dont get what you mean

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Other answers:

look at this http://www.mathsisfun.com/algebra/polynomials.html
here it is ax^3+bx^2+cx+d
so is 5 a and -6.3 b?
nope
how do i determine a an
and b
x=5 and y=-6.3
using the graph u should find a, b, c and d
how so?
is it the right graph?
yes
x intercepts here are 2 and -2
as you can see from the graph another 2 points through which it passes are (0,-2) and (0,2)
this one has a zero at \(-2\) and a zero at \(2\) with multiplicity 2
sorry i mean (2,0) and (-2,0)
making it \[a(x+2)(a-2)^2\] and your last job is to find \(a\)
since you know it goes through \((5,-6.3)\) replace \(x\) by \(5\), set the result equal to \(-6.3\) and solve for \(a\)
so -6.3=(5+2)(a-2)^2?
i am not sure, however, how you know it goes through that point, because it doesn't really look like it
no, you need to solve for \(a\)
replace \(x\) by \(5\) not by \(a\)
\[ -6.3=a(5+2)(5-2)^2\]
\[-6.3=7\times 9 a\] etc
so a=-0.1
??
-6.3 / 63 = - 0.1 yes
so ax^3+bx^2+cx+d how do i fit all this into this format
expand -0.1(x +2)(x - 2)^2
-0.1x^3 + 0.2x^2 + 0.4x - 0.8???
yes
one last one
The curve above is the graph of a degree 4 polynomial. It goes through the point (5,−202.5). Find the polynomial
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satellite confused me at first when in his 2nd post he typed a instead of x. he made a human error which we all can make sometimes.
oh ok
this can be dome in similar way to the first curve there are zeros at =4 and 2 and at x=0 with duplicity 2
i meant -4
so we can write a(x+4)(x - 2)(x- 0)^2 or ax^2(x+4)(x-2)
can you continue from here?
you now need to use x = 5 y = -202.5
ive got 675 for a
-202.5 = 25a * 9 * 3 = -202.5 / (25*27)
cant be 675
-0.3?
oh ok
so you need to expand -0.3 x^2(x + 4\)(x - 2)
thanks
yw

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