If we express $-2x^2 + 4x + 5$ in the form $a(x - h)^2 + k$, then what is $k$?
+9488 If we express −2x2+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
+9488 If we express −2x2+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
