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

- anonymous

- katieb

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- anonymous

##### 1 Attachment

- anonymous

a sum of several terms produces a polynomial

- anonymous

i dont get what you mean

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- anonymous

look at this http://www.mathsisfun.com/algebra/polynomials.html

- anonymous

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

- anonymous

so is 5 a and -6.3 b?

- anonymous

nope

- anonymous

how do i determine a an

- anonymous

and b

- anonymous

x=5 and y=-6.3

- anonymous

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

- anonymous

how so?

- anonymous

is it the right graph?

- anonymous

yes

- anonymous

x intercepts here are 2 and -2

- cwrw238

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

- anonymous

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

- cwrw238

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

- anonymous

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

- 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

so -6.3=(5+2)(a-2)^2?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

so a=-0.1

- anonymous

??

- cwrw238

-6.3 / 63 = - 0.1 yes

- anonymous

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

- cwrw238

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

- anonymous

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

- cwrw238

yes

- anonymous

one last one

- anonymous

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

- anonymous

##### 1 Attachment

- 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

oh ok

- 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

i meant -4

- cwrw238

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

- cwrw238

can you continue from here?

- cwrw238

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

- anonymous

ive got 675 for a

- cwrw238

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

- cwrw238

cant be 675

- cwrw238

-0.3?

- anonymous

oh ok

- cwrw238

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

- anonymous

thanks

- cwrw238

yw

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