Posted by **gabs** on Tuesday, June 7, 2011 at 7:14pm.

Find an equation of the cubic polynomial f(x) = ax3 + bx2 + cx + d that passes through the given points.

P(0,-4) Q(1,-8) R(-1,-8) S(2,-2)

Ive tried this every which way and i cant seem to get any of these..i know your supposed to plug it in and all but its just not working for me. can someone help me and write out the steps for me pleasee!

- pre calc -
**Reiny**, Tuesday, June 7, 2011 at 8:36pm
sub in each of the points to get

-4 = 0+0+0+d , so we know d = -4

-8 = a+b+c - 4 ---> a+b+c = -4

-8 = -a + b -c-4 ---> -a + b-c = -4

let's add these last two : 2b = -8 or b = -4

last point:

-2 = 8a +4b + 2c - 4

8a -16 + 2c - 4 = 2

4a -8 + c = 1 or c = -4a+9

sub into a+b+c=-4

a -4 + (-4a + 9) = -4

-3a = -9

a=3 and finally c = -12+9 = -3

so f(x) = 3x^3 -4x^2 - 3x - 4

I will leave it up to you to sub in the given points, I think they all work

BTW, the above is not the only way to do it, I sort of just let it flow.

- pre calc -
**Mgraph**, Tuesday, June 7, 2011 at 8:53pm
Solve the system:

a*0^3+b*0^2+c*0+d=-4

a*1^3+b*1^2+c*1+d=-8

a*(-1)^3+b+(-1)^2+c*(-1)+d=-8

a*2^3+b*2^2+c*2+d=-2

d=-4

a+b+c+d=-8

-a+b-c+d=-8

8a+4b+2c+d=-2

Add the 2nd and the 3rd: 2b+2d=-16

d=-4

b=-4

a+c=0

8a+2c=18

Subtract from the 4th 2*3rd: 6a=18

a=3, b=-4, c=-3, d=-4

## Answer This Question

## Related Questions

- calculus - Find a cubic function y = ax3 + bx2 + cx + d whose graph has ...
- Calc - Find a cubic function, in the form below, that has a local maximum value ...
- algebra 2 - Question: Write the equation of a cubic function that has the x-...
- Math, 11 - okay so i am trying to model a cubic equation to fit my curve my base...
- Math - Find the equation for the exponential function that passes through the ...
- pre calc - A polynomial f(x) with real coefficients and leading coefficient 1 ...
- math - i have more than one question so if u no any of the answers please tell ...
- Algebra ?? - What would be the missing piece of information given the following ...
- Pre-calc - find a possible polynomial equation of degree 4 if the zeroes are -1,...
- pre calculus - find an equation of the line that passes through the points (0,0...

More Related Questions