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What real value of \(t\) produces the smallest value of the quadratic \(t^2 -9t - 36 \)?
 

 Feb 19, 2020
 #1
avatar+219 
0

Hey @pinklemonade!

 

Use the factoring method to get -3 as the answer for t.

 

Cheers!laugh

 Feb 19, 2020
 #2
avatar+109740 
+1

The  "t"  that produces the smallest value is at the vertex of this parabola.....this is

 

- (-9) / [ -2 *1 ]  =  9/2  = 4.5

 

See the graph here :  (I've used x instead of t....but....same idea) :

 

https://www.desmos.com/calculator/jzlppgwsly

 

 

cool cool cool

 Feb 19, 2020
 #3
avatar+219 
+1

@CPhill, are you sure it is 4.5?

Hypotenuisance  Feb 19, 2020
 #4
avatar+109740 
+1

Yeah....look at the graph I cited in my answer

 

When   t  = 4.5   the  graph is at its minimum =  -56.25

 

So....t =4.5  produces the minimum value of the quadratic

 

 

cool cool cool

CPhill  Feb 19, 2020

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