SOLUTION: In the xy plane, the point (-1,2) is the minimum of the quadratic function f(x)=x^2+ax+b. What's the absolute value of a-2b?

Algebra ->  Finance -> SOLUTION: In the xy plane, the point (-1,2) is the minimum of the quadratic function f(x)=x^2+ax+b. What's the absolute value of a-2b?      Log On


   

Question 1088882: In the xy plane, the point (-1,2) is the minimum of the quadratic function f(x)=x^2+ax+b. What's the absolute value of a-2b?
Found 3 solutions by Fombitz, MathTherapy, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If it's the minimum value, then it's the vertex.
f%28x%29=%28x%2B1%29%5E2%2B2
f%28x%29=x%5E2%2B2x%2B1%2B2
f%28x%29=x%5E2%2B2x%2B3
So then,
a-2b=2-2%283%29
a-2b=2-6
a-2b=-4

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
In the xy plane, the point (-1,2) is the minimum of the quadratic function f(x)=x^2+ax+b. What's the absolute value of a-2b?
Correct answer: highlight_green%284%29, since the question asks for the ABSOLUTE VALUE of a - 2b. 

a - b = - 4, but |a - 2b| = 4.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
If it's the minimum value, then it's the vertex.
f%28x%29=%28x%2B1%29%5E2%2B2
f%28x%29=x%5E2%2B2x%2B1%2B2
f%28x%29=x%5E2%2B2x%2B3

So then a = 2, b = 3

a - 2b = 2 - 2*3 = 2 - 6 = -4.

Absolute value of (a-2b) is 4.