SOLUTION: Determine whether a quadratic model exists for the set of the values below. If so, write the model. f(0)=4, f(3)=-17, f(-1)=-1

Question 935908: Determine whether a quadratic model exists for the set of the values below. If so, write the model. f(0)=4, f(3)=-17, f(-1)=-1

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
general form of quadratic is
ax^2 +bx +c, where a, b, c are constants
we are given that f(0)=4, f(3)=-17, f(-1)=-1
1) f(0)=4
a*0 + b*0 +c = 4
c=4
2) f(3)=-17
9a +3b + 4 = -17
9a +3b = -21
3) f(-1) = -1
a -b +4 = -1
a -b = -5
the two equations we have are
9a +3b = -21
a -b = -5
multiply the second equation by 3 and then add the result ot the first equation
12a = -36
a = -3
substitute for a in second equation
-3 -b = -5
-b = -2
b = 2
our quadratic equation is
-3x^2 +2x +4
to check the quadratic formula calculate f(0), f(3), f(-1)
f(0) = 0 + 0 +4 = 4
f(3) = -27 +6 +4 = -17
f(-1) = -3 -2 +4 = -1
our formula checks, therefore it is correct

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