Breno
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



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Breno
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SerikMB
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a sum of several terms produces a polynomial

Breno
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i dont get what you mean


SerikMB
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here it is ax^3+bx^2+cx+d

Breno
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so is 5 a and 6.3 b?

SerikMB
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nope

Breno
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how do i determine a an

Breno
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and b

SerikMB
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x=5 and y=6.3

SerikMB
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using the graph u should find a, b, c and d

Breno
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how so?

SerikMB
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is it the right graph?

Breno
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yes

SerikMB
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x intercepts here are 2 and 2

cwrw238
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as you can see from the graph another 2 points through which it passes are
(0,2) and (0,2)

anonymous
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this one has a zero at \(2\) and a zero at \(2\) with multiplicity 2

cwrw238
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sorry i mean (2,0) and (2,0)

anonymous
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making it
\[a(x+2)(a2)^2\] and your last job is to find \(a\)

anonymous
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since you know it goes through \((5,6.3)\) replace \(x\) by \(5\), set the result equal to \(6.3\) and solve for \(a\)

Breno
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so 6.3=(5+2)(a2)^2?

anonymous
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i am not sure, however, how you know it goes through that point, because it doesn't really look like it

anonymous
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no, you need to solve for \(a\)

anonymous
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replace \(x\) by \(5\) not by \(a\)

anonymous
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\[ 6.3=a(5+2)(52)^2\]

anonymous
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\[6.3=7\times 9 a\] etc

Breno
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so a=0.1

Breno
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??

cwrw238
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6.3 / 63 =  0.1 yes

Breno
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so ax^3+bx^2+cx+d
how do i fit all this into this format

cwrw238
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expand
0.1(x +2)(x  2)^2

Breno
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0.1x^3 + 0.2x^2 + 0.4x  0.8???

cwrw238
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yes

Breno
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one last one

Breno
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The curve above is the graph of a degree 4 polynomial. It goes through the point (5,−202.5). Find the polynomial

Breno
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cwrw238
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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.

Breno
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oh ok

cwrw238
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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
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i meant 4

cwrw238
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so we can write
a(x+4)(x  2)(x 0)^2
or ax^2(x+4)(x2)

cwrw238
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can you continue from here?

cwrw238
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you now need to use x = 5 y = 202.5

Breno
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ive got 675 for a

cwrw238
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202.5 = 25a * 9 * 3
= 202.5 / (25*27)

cwrw238
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cant be 675

cwrw238
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0.3?

Breno
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oh ok

cwrw238
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so you need to expand
0.3 x^2(x + 4\)(x  2)

Breno
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thanks

cwrw238
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yw