Vertex location identification from evaluated conditions
The question provides evaluated values of a quadratic at specific points and asks the student to determine or select the location (e.g., x-coordinate range) of the vertex, using completing the square or axis-of-symmetry reasoning.
Given that a real-coefficient quadratic polynomial function $f ( x )$ satisfies $f ( - 1 ) = k , f ( 1 ) = 9 k , f ( 3 ) = - 15 k$, where $k > 0$. Let the $x$-coordinate of the vertex of the graph of $y = f ( x )$ be $a$. Select the correct option. (1) $a \leq - 1$ (2) $- 1 < a < 1$ (3) $a = 1$ (4) $1 < a < 3$ (5) $3 \leq a$