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# If \$t\$ is a real number, what is the maximum possible value of the expression \$-t^2 + 8t -4\$?

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If \$t\$ is a real number, what is the maximum possible value of the expression \$-t^2 + 8t -4\$?

Guest Jan 23, 2018

#1
+6939
+2

the maximum value occurs when...

t   =   -8 / [ 2(-1) ]

t   =   -8 / -2

t   =   4

When  t  =  4 ...

-t2 + 8t - 4

=  -42 + 8(4) - 4

=  -16 + 32 - 4

=  12

Here's a graph:   https://www.desmos.com/calculator/qdghoci3o9

hectictar  Jan 23, 2018
Sort:

#1
+6939
+2

the maximum value occurs when...

t   =   -8 / [ 2(-1) ]

t   =   -8 / -2

t   =   4

When  t  =  4 ...

-t2 + 8t - 4

=  -42 + 8(4) - 4

=  -16 + 32 - 4

=  12

Here's a graph:   https://www.desmos.com/calculator/qdghoci3o9

hectictar  Jan 23, 2018

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