True or False: The quadratic function y = -x^2 - 12x - 36, which can be used to model a company's production cost deviation, has exactly one x-intercept at the point (-6, 0).

A quality control technician uses the quadratic model $y = -x^2 - 12x - 36$ to analyze the deviation in a production process. To find the x-intercept (the point where the deviation is zero), the technician must follow a specific algebraic sequence. Arrange the following steps in the correct order as they would appear in the solution process.

An operations manager uses the quadratic function $y = -x^2 - 12x - 36$ to model the deviation in production costs. Match each component of the model's intercepts with its correct numerical value.

Identifying Zero-Deviation Points in Quality Control

Inventory Deviation Analysis

An industrial engineer uses the model $y = -x^2 - 12x - 36$ to represent the deviation in a conveyor belt's speed. After factoring the equation into $0 = -(x + 6)^2$ to find the x-intercept, the engineer applies the ____ Property to solve for the value of $x$.

Documentation of Intercept Analysis for Performance Models

A technician uses the quadratic function $y = -x^2 - 12x - 36$ to model the cost deviation of a production line. To find the point of zero deviation (the x-intercept), the technician must factor the equation. According to the solution process for this specific model, which of the following is the correct factored form of the equation?

Identify the structure of $x^2 + 12x + 36$ when finding x-intercepts

Finding the y-intercept of $y = -x^2 - 12x - 36$