Find the coordinates of the vertex of the quadratic function.
-$$f ( x ) = - x ^ { 2 } - 8 x + 1$$
A) $( - 8,1 )$
B) $( - 4,17 )$
C) $( 4 , - 47 )$
D) $( 4 , - 15 )$

Question

Quizplus · Accepted Answer

The vertex of a quadratic function in the form $f(x) = ax^2 + bx + c$ can be found using the formula $(- \frac{b}{2a}, f(- \frac{b}{2a}))$. For the given function, $a = -1$, $b = -8$, and $c = 1$. Thus, the x-coordinate of the vertex is $- \frac{-8}{2(-1)} = -4$. Substituting $x = -4$ into the function gives $f(-4) = -(-4)^2 - 8(-4) + 1 = -16 + 32 + 1 = 17$. Therefore, the vertex is $(-4, 17)$.

Find the Coordinates of the Vertex of the Quadratic Function f(x)=−x2−8x+1f ( x ) = - x ^ { 2 } - 8 x + 1f(x)=−x2−8x+1

Find the Coordinates of the Vertex of the Quadratic Function $f ( x ) = - x ^ { 2 } - 8 x + 1$