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What real value of t produces the smallest value of the quadratic t^2 + 9t - 36 - 7t + 45?

 Feb 3, 2021
 #1
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We first combine like terms and get:

 

\(x^2 + 2x + 9\)

 

Then, we complete the square to get:

 

\(x^2 + 2x + 1 + 8\)

 

\((x+1)^2 + 8\)

 

Therefore, the minimum value of x is equal to -1

 

Oops sorry I replaced x with t

 Feb 3, 2021
 #2
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+1

t^2 +2t +9       will have a minumum value at    t = - b/2a    =  - 2/2 = -1   

 Feb 3, 2021

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