Try It: Solving $x^2 + 2x - 8 < 0$ Graphically

Try It: Solving $x^2 - 8x + 12 \geq 0$ Graphically

A business owner uses the quadratic function $f(x) = x^2 - 6x + 8$ to model the daily operating costs of a small delivery service. To identify when the costs fall below a target threshold ($x^2 - 6x + 8 < 0$), the owner analyzes the graph of the cost function. Based on the specific analysis of this model provided in the lesson, match each graphical component with its correct coordinates.

A project manager uses the quadratic function $f(x) = x^2 - 6x + 8$ to model the projected cost variance of a new initiative over $x$ months. The project is considered 'under budget' when the variance is negative ($x^2 - 6x + 8 < 0$). Based on the graphical analysis of this upward-opening parabola, which has $x$-intercepts at 2 and 4, which interval correctly identifies the months during which the project is under budget?

A supply chain manager uses the function $f(x) = x^2 - 6x + 8$ to model operational variance. When solving the inequality $x^2 - 6x + 8 < 0$ graphically, the $x$-intercepts (2, 0) and (4, 0) are included as part of the solution set.

A project manager uses the quadratic function $f(x) = x^2 - 6x + 8$ to model monthly budget variances. To solve the inequality $x^2 - 6x + 8 < 0$ graphically and identify when the project is under budget, arrange the following steps in the correct order as described in the course example.

A data analyst for a logistics company is evaluating a cost model given by the quadratic function $f(x) = x^2 - 6x + 8$, where $x$ represents time in months. The company operates at a net loss when this model is strictly less than zero ($x^2 - 6x + 8 < 0$). By recalling the graphical analysis of this specific upward-facing parabola, the graph falls strictly below the $x$-axis between its $x$-intercepts of 2 and 4. Therefore, the solution to this inequality in interval notation is ____.

Key Graphical Features of a Deficit Model

Recalling the Graphical Solution of a Quadratic Cost Variance Model