Question

Can someone please help me find the cubic equation of a graph with the coordinates: (0,1) (1,2.5) (3,1) (4.5,4)

Answer 1

If you have four distinct points in the xy-plane, and no two x-coordinates are equal, then there is a unique cubic equation of the form

y = ax³ + bx² + cx + d

that passes through the four points.

Answer 2

For (0,1), x = 0 and y = 1.

y = ax³ + bx² + cx + d

becomes for that point:

1 = a*0³ + b*0² + c*0 + d

1 = 0 + 0 + 0 + d

d = 1

That leaves a, b, and c to find.

Answer 3

For (1, 2.5), x = 1 and y = 2.5

For that point, y = ax³ + bx² + cx + d becomes:

2.5 = a*1³ + b*1² + c*1 + d

d is known to be 1

2.5 = a + b + c + 1

1.5 = a + b + c

Answer 4

Go through this procedure twice more, once for (3,1) and once for (4.5,4).

@kmeezy

Answer 5

I did and I got
0= 9a+3b+c
and
3= 91.125a+20.25b+4.5c
but i do not know how to proceed after this
Also I have attached the graph over here

Answer 6

@Directrix

Answer 7

For the third equation, I got this;

0= 27*a + 9*b + 3*c

Answer 8

Yeah i simplified it, if that is right?

Answer 9

We have 3 equations in 3 unknowns so we have to solve that system for a, b, and c.

1.5 = a + b + c

0 = 9*a+3*b + c

3= 91.125*a + 20.25*b + 4.5*c

Answer 10

I think c is the easiest variable to eliminate.

That would suppress the system to a 2 by 2 system.

Answer 11

Are you supposed to show all the work on this?

Answer 12

Maybe this is very complicated because I do not know the accurate coordinates, did you see the graph? No actually i have to plot the second derivative of this graph.

Answer 13

>>Can someone please help me find the cubic equation of a graph with the coordinates: (0,1) (1,2.5) (3,1) (4.5,4)

I worked on the posted question. If you need to plot the curve of the second derivative,
then I think you should crank out the values of a, b, and c in the 3 by 3 system.

Then, you can write the exact equation of the function.

After that, take its derivate and draw the graph of that.

Answer 14

I have figured out the equation it is : 1/3x^3-2x^2+3x+1
Now the derivative part is easy
Thank you so much for helping!

Answer 15

You are welcome.