Express the function in the formss the function in the form f(x) $$f ( x ) = a ( x - h ) ^ { 2 } + k$$ k a nd indicate the vertex.
-$$f ( x ) = - x ^ { 2 } + 2 x + 7$$
A) $f ( x ) = - ( x - 1 ) ^ { 2 } + 8$
vertex: $( 1,8 )$
B) $f ( x ) = - ( x + 1 ) ^ { 2 } + 6$
vertex: $( - 1,6 )$
C) $f ( x ) = - ( x - 2 ) ^ { 2 } + 7$
vertex: $( 2,7 )$
D) $f ( x ) = - ( x + 1 ) ^ { 2 } + 4$
vertex: $( - 1,4 )$

Question

Quizplus · Accepted Answer

The given function $f(x) = -x^2 + 2x + 7$ can be rewritten in vertex form by completing the square. The coefficient of $x^2$ is -1, so we factor this out from the first two terms: $-1(x^2 - 2x) + 7$. Completing the square inside the parentheses gives us $-1[(x - 1)^2 - 1^2] + 7$, which simplifies to $-1(x - 1)^2 + 8$, matching option A. The vertex form $f(x) = a(x - h)^2 + k$ reveals the vertex as $(h, k)$, so the vertex here is $(1, 8)$.

Express the Function in the Formss the Function in the Form