SOLUTION: use the given values to find an equation of the form f(x)=ax^2 + bx + c 3. f(0)= 6, f(2)= 18, f(4)= 34 Please explain step by step! I would really appreciate any help!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: use the given values to find an equation of the form f(x)=ax^2 + bx + c 3. f(0)= 6, f(2)= 18, f(4)= 34 Please explain step by step! I would really appreciate any help!       Log On


   

Question 172693: use the given values to find an equation of the form f(x)=ax^2 + bx + c
3. f(0)= 6, f(2)= 18, f(4)= 34
Please explain step by step!
I would really appreciate any help!
Thank you very much!
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=ax^2 + bx + c
f(0)=6
f(0)=a*0^2+b*0+c
f(0)=c thus c=6
f(2)=18
f(2)=a*2^2+b*2+6
f(2)=4a+2b+6=18 multiply by -4 & add to the f(4) equation
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f(4)=34
f(4)=a*4^2+b*4+6
f(4)=16a+4b+6=34
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-16a-8b-24=-72
16a+4b+6=34 add.
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-4b-18=-38
-4b=-38+18
-4b=-20
b=-20/-4
b=5 ans.
4a+2*5+6=18
4a+10+6=18
4a=18-10-6
4a=2
a=2/4=1/2=.5 ans.
Proof
16*.5+4*5+6=34
8+20+6=34
34=34
f(x)=a/2+5b+6