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

WhichWitchIsWhich  Oct 29, 2017
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 #1
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+2

x^2 + 3x + c

 

To have -2 remain in the range...since this parabola turns upward..it must be that the vertex is at (a, -2)

 

The x coordinate of the vertex  is given by   -3/  [2 * 1]  =  -3/2

 

So.....it must be that

 

(-3/2)^2  + 3(-3/2)  + c  = -2  simplify

 

9/4  - 9/2  + c  =  -2

 

-9/4  +  c  =  -2

 

-9/4  + c  =  -8/4    add 9/4 to both sides

 

1/4  =  c   ⇒   any larger value takes -2 out of the range

 

See the graph here : https://www.desmos.com/calculator/b25akxl65z

 

 

cool cool cool

CPhill  Oct 29, 2017

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