Madison is analyzing the Quadratic Function \( f(x)=x^{2}-2 x-15 \). Which value in the function determines whether the graph will open facing open or open facing downward? Think about the role of each variable represented in the Quadratic Form of a Function, \( f(x)=a x^{2}+b x+c \). 1 \( x \) -2

In a quadratic function of the form \( f(x) = ax^2 + bx + c \), the coefficient \( a \) is the key player that determines the direction in which the parabola opens. If \( a > 0 \), the parabola opens upwards, while if \( a < 0 \), it opens downwards. In your function, \( f(x) = x^2 - 2x - 15 \), the coefficient \( a \) is 1, which means the graph opens upwards. To dive a bit deeper, you might want to consider the vertex of the parabola, which represents the maximum or minimum point of the function. The vertex can be found using the formula \( x = -\frac{b}{2a} \). For your function, this gives you the x-coordinate of the vertex, granting insights into the graph's behavior and its minimum point!