SOLUTION: use the given values to find an equation of the form f(x)= ax^2 + bx + c 1. f(0)= 5, f(1)=10, f(2)= 19 Please explain step by step so I understand! I would really appreci

Question 172691: use the given values to find an equation of the form f(x)= ax^2 + bx + c
1. f(0)= 5, f(1)=10, f(2)= 19
Please explain step by step so I understand!
I would really appreciate any help!
Thank you very much
Found 2 solutions by checkley77, solver91311:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
f(x)= ax^2 + bx + c
f(0)= 5
f(0)=a*0^2+b*0+c=5
f(0)=0+0+c=5
f(0)c=5 ans.
f(1)=10
f(1)=a*1^2+b*1+5
f(1)a+b+5=10 multiply this equation by -2 & add.
f(2)= 19
f(2)=a*2^2+b*2+5
f(2)4a+2b+5=19
------------------------------
-2a-2b-10=-20
4a+2b+5=19 add.
-----------------
2a-5=-1
2a=-1+5
2a=4
a=4/2
a=2 ans.
2+b+5=10
b=10-5-2
b=3 ans.
Proof:
4*2+2*3+5=19
8+6+5=19
19=19
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If is a function, then is the value of the function evaluated at . You are given the values of the function evaluated at 0, 1, and 2. So:
(1) means that , simplified

(2) means that , simplified

(3) means that , simplified

Since from (1) we have , that can be substituted into (2) and (3), thus:

(4) yielding and,

(5) yielding yielding

Multiply (5) by :

(6)

Add (6) to (4) term-by-term:

(7) or

Substitute into (4):

(8) or

Now you can say that by substituting the values determined for , , and when the system of linear equations was solved.

Check:
Check

Check

Check
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