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If we express \(-2x^2 + 4x + 5\) in the form \(a(x - h)^2 + k\), then what is \(k\)?

 Jul 16, 2019
 #1
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-2x^2 + 4x + 5       factor out the "-2"

 

-2 ( x^2 - 2x  - 5/2)      

 

Complete the square on x......take (1/2) of 2  = 1....square iy 1^2  = 1....add and subtract it within the parentheses

 

-2 ( x^2  - 2x + 1 - 5/2 - 1)     factor the first three terms in the parentheses.....simplify the rest

 

-2 [ ( x - 1)^2   -  7/2 ]      distribute the "-2"  

 

-2 ( x - 1)^2 +  7

 

k = 7

 

 

cool cool cool

 Jul 16, 2019

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