Find the vertex and axis of symmetry of the graph of the function.
-$$f ( x ) = - x ^ { 2 } + 6 x$$
A) $( 3,9 ) ; x = 3$
B) $( - 3 , - 9 ) ; x = - 3$
C) $( 9 , - 3 ) ; x = 9$
D) $( - 9,3 ) ; x = - 9$

Question

Quizplus · Accepted Answer

The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For the given function $f(x) = -x^2 + 6x$, we can complete the square to find the vertex. First, factor out the coefficient of $x^2$, which is -1: $$f(x) = -(x^2 - 6x).$$ To complete the square, add and subtract $\left(\frac{6}{2}\right)^2 = 9$ inside the parenthesis: $$f(x) = -(x^2 - 6x + 9 - 9).$$ Simplify to get $$f(x) = -(x - 3)^2 + 9.$$ Thus, the vertex is $(3, 9)$. The axis of symmetry is the line that passes through the vertex, which is $x = 3$.

Find the Vertex and Axis of Symmetry of the Graph f(x)=−x2+6xf ( x ) = - x ^ { 2 } + 6 xf(x)=−x2+6x

Find the Vertex and Axis of Symmetry of the Graph $f ( x ) = - x ^ { 2 } + 6 x$