Find the vertex of the graph of the quadratic function.
-$$f ( x ) = x ^ { 2 } + 14 x - 9$$
A) $( 7,138 )$
B) $( 14,383 )$
C) $( - 7 , - 156 )$
D) $( - 7 , - 58 )$

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 $(- \frac{b}{2a}, f(- \frac{b}{2a}))$. Here, $a = 1$, $b = 14$, and $c = -9$. Thus, the x-coordinate of the vertex is $- \frac{14}{2 \cdot 1} = -7$. Substituting $x = -7$ into the function gives $f(-7) = (-7)^2 + 14(-7) - 9 = 49 - 98 - 9 = -58$. Therefore, the vertex is $(-7, -58)$.

Find the Vertex of the Graph of the Quadratic Function f(x)=x2+14x−9f ( x ) = x ^ { 2 } + 14 x - 9f(x)=x2+14x−9

Find the Vertex of the Graph of the Quadratic Function $f ( x ) = x ^ { 2 } + 14 x - 9$