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

Jun 25, 2019

#1
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If we express  \(-2x^2 + 4x + 5\)  in the form  \(a(x - h)^2 + k\) ,  then what is  \(k\) ?

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=   -2x2 + 4x + 5

Factor  -2  out of the first two terms.

=   -2( x2 - 2x ) + 5

Add  1  and subtract  1  to complete the square inside the parenthesees.

=   -2( x2 - 2x + 1 - 1 ) + 5

Factor  x2 - 2x + 1  as  (x - 1)2

=   -2( (x - 1)2 - 1 ) + 5

Distribute the  -2

=  -2(x - 1)2 + 2 + 5

Combine like terms.

=  -2(x - 1)2 + 7

Now it is in the form  a(x - h)2 + k  and we can see that  k = 7

Jun 25, 2019

#1
+5

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

----------

=   -2x2 + 4x + 5

Factor  -2  out of the first two terms.

=   -2( x2 - 2x ) + 5

Add  1  and subtract  1  to complete the square inside the parenthesees.

=   -2( x2 - 2x + 1 - 1 ) + 5

Factor  x2 - 2x + 1  as  (x - 1)2

=   -2( (x - 1)2 - 1 ) + 5

Distribute the  -2

=  -2(x - 1)2 + 2 + 5

Combine like terms.

=  -2(x - 1)2 + 7

Now it is in the form  a(x - h)2 + k  and we can see that  k = 7

hectictar Jun 25, 2019