pre calc
posted by gabs .
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!

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 c4 > a + bc = 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. 
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+bc+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
Respond to this Question
Similar Questions

Calc
Find a cubic function, in the form below, that has a local maximum value of 3 at 2 and a local minimum value of 0 at 1. f (x) = ax3 + bx2 + cx + d 
Math, 11
okay so i am trying to model a cubic equation to fit my curve my base curve is specifications: x value0 to 6.19 amplitude0.77 amplitude coordinates3.73,0.77 x intercepts0,0 and 6.19 , 0 this is my curve and i have to make a equation … 
Maths
Hi, need a bit of help on this one. A straight line passes through the points (4,3) and (10,0), I need to write down the equation of the line in the form y=mx+c, I have tried but I cant seem to get the second coordinates to satisfy … 
Math
Find the equation for the exponential function that passes through the pairs of points given. Through (1,2) and (3,1). I don't know if this is the right way to work this or what the next step is i am just very confused. Please help, … 
calculus
Find a cubic function y = ax3 + bx2 + cx + d whose graph has horizontal tangents at the points 
algebra 2
Question: Write the equation of a cubic function that has the xintercepts of 4, 2, and 5 and passes through the point (6,20) My Answer: y = .5x^31.5x^29x+20 What I did: Put the xintercepts and given point into stat plot (on calculator) … 
Pre calc
Find an equation of the line that passes through the given points. (Let x be the independent variable and y be the dependent variable.) (3, 13) and (4, 20) 
pre Calc
Find an equation of the vertical line that passes through (x, y) = (−3, 4). 
precalc
If p(3) = p(1) = p(2)= 0 and p(0) =6 find the cubic polynomial 
precalc
Find a cubic polynomial if p(0)=0 and p(2)= 4 and p(x) > 0 only if x > 4, find the cubic polynomial.