anonymous
  • anonymous
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
katieb
  • katieb
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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
a sum of several terms produces a polynomial
anonymous
  • anonymous
i dont get what you mean

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anonymous
  • anonymous
look at this http://www.mathsisfun.com/algebra/polynomials.html
anonymous
  • anonymous
here it is ax^3+bx^2+cx+d
anonymous
  • anonymous
so is 5 a and -6.3 b?
anonymous
  • anonymous
nope
anonymous
  • anonymous
how do i determine a an
anonymous
  • anonymous
and b
anonymous
  • anonymous
x=5 and y=-6.3
anonymous
  • anonymous
using the graph u should find a, b, c and d
anonymous
  • anonymous
how so?
anonymous
  • anonymous
is it the right graph?
anonymous
  • anonymous
yes
anonymous
  • anonymous
x intercepts here are 2 and -2
cwrw238
  • cwrw238
as you can see from the graph another 2 points through which it passes are (0,-2) and (0,2)
anonymous
  • anonymous
this one has a zero at \(-2\) and a zero at \(2\) with multiplicity 2
cwrw238
  • cwrw238
sorry i mean (2,0) and (-2,0)
anonymous
  • anonymous
making it \[a(x+2)(a-2)^2\] and your last job is to find \(a\)
anonymous
  • anonymous
since you know it goes through \((5,-6.3)\) replace \(x\) by \(5\), set the result equal to \(-6.3\) and solve for \(a\)
anonymous
  • anonymous
so -6.3=(5+2)(a-2)^2?
anonymous
  • anonymous
i am not sure, however, how you know it goes through that point, because it doesn't really look like it
anonymous
  • anonymous
no, you need to solve for \(a\)
anonymous
  • anonymous
replace \(x\) by \(5\) not by \(a\)
anonymous
  • anonymous
\[ -6.3=a(5+2)(5-2)^2\]
anonymous
  • anonymous
\[-6.3=7\times 9 a\] etc
anonymous
  • anonymous
so a=-0.1
anonymous
  • anonymous
??
cwrw238
  • cwrw238
-6.3 / 63 = - 0.1 yes
anonymous
  • anonymous
so ax^3+bx^2+cx+d how do i fit all this into this format
cwrw238
  • cwrw238
expand -0.1(x +2)(x - 2)^2
anonymous
  • anonymous
-0.1x^3 + 0.2x^2 + 0.4x - 0.8???
cwrw238
  • cwrw238
yes
anonymous
  • anonymous
one last one
anonymous
  • anonymous
The curve above is the graph of a degree 4 polynomial. It goes through the point (5,−202.5). Find the polynomial
anonymous
  • anonymous
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cwrw238
  • cwrw238
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.
anonymous
  • anonymous
oh ok
cwrw238
  • cwrw238
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
cwrw238
  • cwrw238
i meant -4
cwrw238
  • cwrw238
so we can write a(x+4)(x - 2)(x- 0)^2 or ax^2(x+4)(x-2)
cwrw238
  • cwrw238
can you continue from here?
cwrw238
  • cwrw238
you now need to use x = 5 y = -202.5
anonymous
  • anonymous
ive got 675 for a
cwrw238
  • cwrw238
-202.5 = 25a * 9 * 3 = -202.5 / (25*27)
cwrw238
  • cwrw238
cant be 675
cwrw238
  • cwrw238
-0.3?
anonymous
  • anonymous
oh ok
cwrw238
  • cwrw238
so you need to expand -0.3 x^2(x + 4\)(x - 2)
anonymous
  • anonymous
thanks
cwrw238
  • cwrw238
yw

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