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avatar+458 

Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-3x+8$.

 Mar 7, 2024
 #1
avatar+128406 
+1

x^2 - 8x + 8 + c

 

The x coordinate of the vertex is   8/ (2*1)  = 4

 

So....we  need y to be 1  when x  = 4

 

1  = (4)^2 - 8(4) + 8 + c

 

1 = 16 - 32 + 8 + c

 

1 = -8 + c

 

c  =  9

 

Here's the graph :

 

Note that  if c is larger than 9, the graph is  shited above y =1....so 1 will not be in the range

 

 

cool cool cool

 Mar 7, 2024

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