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Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-13x+27$.

 Jan 13, 2024
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y  =   x^2 -18x + 27 + c

 

We want to find the vertex  of

 

x^2 -18x + 27

 

x coordinate of the  vertex   =  -(-18) /(2 * 1)   = 9

 

Put this  back into  the  function  to  find the y coordinate ofthe  vertex

9^2 - 18(9) + 27 =  -54

 

So  ....to find c

 

-54  + c = 1

 

c  = 55

 

cool cool cool

 Jan 13, 2024

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