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 of a parabola in the form $f(x) = ax^2 + bx + c$ can be found using the formula $(- \frac{b}{2a}, f(- \frac{b}{2a}))$. Here, $a = 1$ and $b = 6$, so the x-coordinate of the vertex is $- \frac{6}{2(1)} = -3$. Plugging this back into the function gives $f(-3) = (-3)^2 + 6(-3) = 9 - 18 = -9$, so the vertex is $(-3, -9)$. The axis of symmetry is always $x = - \frac{b}{2a}$, 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 $f ( x ) = x ^ { 2 } + 6 x$