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) $( 9 , - 3 ) ; x = 9$
C) $( - 9,3 ) ; x = - 9$
D) $( - 3 , - 9 ) ; x = - 3$

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. To find the vertex of the given function $f(x) = x^2 + 6x$, we complete the square. First, factor out the coefficient of $x^2$ (which is 1 in this case, so it doesn't change anything). We have $x^2 + 6x$. To complete the square, add and subtract $(\frac{6}{2})^2 = 9$, getting $x^2 + 6x + 9 - 9$. This simplifies to $(x + 3)^2 - 9$, so the vertex is at $(-3, -9)$. The axis of symmetry is at $x = h$, which is $x = -3$ in this case.

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 $f ( x ) = x ^ { 2 } + 6 x$