Question

2.10.3 test (cst): functions which of the following could be the system of nonlinear inequalities graphed below? a. $y > x^2 - 5x + 6$ $y < 5$ b. $y geq x^2 - 5x + 6$ $y leq 5$ c. $y > x^2 - 5x + 6$ $y geq 5$ d. $y geq x^2 - 5x + 6$ $y < 5$

Explanation:

Step1: Analyze the parabola boundary

The parabola is a solid line, so the inequality for it uses $\geq$ (since the shaded region is above the parabola, meaning $y$ is greater than or equal to the quadratic function). The quadratic is $y = x^2 - 5x + 6$, so this gives $y\geq x^2 - 5x + 6$.

Step2: Analyze the horizontal line boundary

The horizontal line is dashed, so the inequality uses $<$ (the shaded region is below this line, so $y$ is less than the line's value, which is 5). This gives $y<5$.

Step3: Match to the options

Combine the two inequalities to find the matching option.

Answer:

D. $y\geq x^2 - 5x+6$
$y<5$