Find the vertex and axis of symmetry of the graph of the function.
-$$f ( x ) = - x ^ { 2 } - 10 x$$
A) (5, -25); x = 5
B) (-25, 5); x = -25
C) (25, -5); x = 25
D) (-5, 25); x = -5

Question

Quizplus · Accepted Answer

The vertex form of a quadratic function is $ f(x) = a(x-h)^2 + k $. For $ f(x) = -x^2 - 10x $, the vertex can be found using $ h = -\frac{b}{2a} $. Here, $ a = -1 $ and $ b = -10 $, so $ h = -\frac{-10}{2(-1)} = -5 $. Substitute $ x = -5 $ into the function to find $ k $: $ f(-5) = -(-5)^2 - 10(-5) = -25 + 50 = 25 $. Thus, the vertex is (-5, 25) and the axis of symmetry is $ x = -5 $.

Find the Vertex and Axis of Symmetry of the Graph f(x)=−x2−10xf ( x ) = - x ^ { 2 } - 10 xf(x)=−x2−10x

Find the Vertex and Axis of Symmetry of the Graph $f ( x ) = - x ^ { 2 } - 10 x$