Final answer:
To calculate the x-intercept of the function f(x) = -x^2 - 5x - 6, apply the quadratic formula with coefficients a = -1, b = -5, and c = -6. Calculate and simplify to find two values for x, which represent the x-intercepts of the function.
Step-by-step explanation:
To find the x-intercept of the function f(x) = -x^2 - 5x - 6, we need to solve the equation for f(x) = 0. The x-intercepts occur where the graph of the function crosses the x-axis. Since the given function is a quadratic function, we can apply the quadratic formula, which is x = (-b ± √(b^2 - 4ac))/(2a), where a, b, and c are coefficients from the quadratic equation ax^2 + bx + c = 0.
In this case, a = -1, b = -5, and c = -6. Plugging these into the quadratic formula we get:
x = (-(-5) ± √((-5)^2 - 4(-1)(-6)))/ (2(-1))
After computing the values under the square root and simplifying, we'll get two values for x, which are the x-intercepts of the quadratic function.