A business owner uses the profit function $f(x) = x^2 - 2x - 8$ to analyze daily earnings based on the number of units sold ($x$). The owner needs to find the specific points on the graph where the profit is exactly 7 hundred dollars. Arrange the following mathematical steps in the correct order to solve for $x$ and identify these points.

A quality control engineer uses the function $f(x) = x^2 - 2x - 8$ to monitor the frequency of machine errors, where $x$ represents the number of hours of operation. To identify the specific points on the graph where the error frequency $f(x)$ is exactly 7, which pair of coordinates must be identified?

A business analyst uses the profit model $f(x) = x^2 - 2x - 8$ to track quarterly earnings (in thousands of dollars) based on the number of marketing campaigns ($x$) launched. To determine the number of campaigns needed to reach a profit of exactly 7 thousand dollars, the analyst follows a series of algebraic steps. Match each procedural goal with the correct mathematical expression used in that step.

A logistics manager uses the profit function $f(x) = x^2 - 2x - 8$ to analyze company performance, where $x$ represents the number of active delivery routes. To find the points on the graph where the profit is exactly 7 units, the manager solves the equation ${}7 = x^2 - 2x - 8$. The calculation identifies two points on the graph: (5, 7) and (____, 7). What is the missing $x$-coordinate?

A financial analyst uses the mathematical model $f(x) = x^2 - 2x - 8$ to project a company's revenue growth (in millions of dollars) based on a specific market variable $x$. To determine the scenarios where the revenue projection is exactly 7 million dollars, the analyst sets up the equation ${}7 = x^2 - 2x - 8$ and concludes that the corresponding points on the graph are (4, 7) and $(-2, 7)$.

Investment Growth Target

Production Cost Analysis