SOLUTION: Find the largest value of c such that -2 is in the range of f(x)=x^2+3x+c.

Algebra ->  Functions -> SOLUTION: Find the largest value of c such that -2 is in the range of f(x)=x^2+3x+c.      Log On


   

Question 1089066: Find the largest value of c such that -2 is in the range of f(x)=x^2+3x+c.
Found 2 solutions by htmentor, Fombitz:
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The largest possible value of c will be obtained when the vertex is at y = -2.
Thus df/dx = 0 = 2x + 3 -> x = -3/2
f(-3/2) = -2 = (-3/2)^2 - 3(-3/2) + c -> c = 1/4

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
At the point that -2 is the minimum value, it is the y coordinate of the vertex.
So then complete the square to get into vertex form.
x%5E2%2B3x%2Bc=-2
x%5E2%2B3x%2B%283%2F2%29%5E2%2Bc=-2%2B%283%2F2%29%5E2
%28x%2B3%2F2%29%5E2=-2-c%2B9%2F4
%28x%2B3%2F2%29%5E2=1%2F4-c
At the vertex x=-3%2F2 so,
1%2F4-c=0
c=1%2F4
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