Question

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

Answer 1

a sum of several terms produces a polynomial

Answer 2

i dont get what you mean

Answer 3

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

Answer 4

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

Answer 5

so is 5 a and -6.3 b?

Answer 6

nope

Answer 7

how do i determine a an

Answer 8

and b

Answer 9

x=5 and y=-6.3

Answer 10

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

Answer 11

how so?

Answer 12

is it the right graph?

Answer 13

yes

Answer 14

x intercepts here are 2 and -2

Answer 15

as you can see from the graph another 2 points through which it passes are

(0,-2) and (0,2)

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

so a=-0.1

Answer 27

??

Answer 28

-6.3 / 63 = - 0.1 yes

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

yes

Answer 33

one last one

Answer 34

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

Answer 35

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.

Answer 36

oh ok

Answer 37

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

Answer 38

i meant -4

Answer 39

so we can write

a(x+4)(x - 2)(x- 0)^2

or ax^2(x+4)(x-2)

Answer 40

can you continue from here?

Answer 41

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

Answer 42

ive got 675 for a

Answer 43

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

Answer 44

cant be 675

Answer 45

-0.3?

Answer 46

oh ok

Answer 47

so you need to expand

-0.3 x^2(x + 4\)(x - 2)

Answer 48

thanks

Answer 49

yw