Consider the Quadratic function \( f(x)=x^{2}-5 x-6 \). Its vertex is \( (\square) \) Its largest \( x \)-intercept is \( x=\square \). Its \( y \)-intercept is \( y=\square \)

The vertex of the quadratic function \( f(x) = x^2 - 5x - 6 \) can be found using the vertex formula \( x = -\frac{b}{2a} \). Here, \( a = 1 \) and \( b = -5 \), giving us \( x = \frac{5}{2} = 2.5 \). To find the corresponding \( y \)-coordinate, substitute \( x \) back into the function. The vertex is at \( \left(2.5, -\frac{25}{4} \right) = \left(2.5, -6.25\right) \). Next, to find the largest \( x \)-intercept, we can use the quadratic formula given by \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Plugging in values here gives us two \( x \)-intercepts: \( x = 6 \) and \( x = -1 \). The largest is \( x = 6 \). Lastly, to find the \( y \)-intercept, we evaluate the function at \( x = 0 \): \( f(0) = 0^2 - 5(0) - 6 = -6 \). So the \( y \)-intercept is \( y = -6 \). In summary: - Vertex: \( (2.5, -6.25) \) - Largest \( x \)-intercept: \( x = 6 \) - \( y \)-intercept: \( y = -6 \)