Question

The graph represents the projected profits for a company, y, based on the number of units sold, x. On a coordinate plane, a parabola with a dashed boundary line opens down. It goes through (15, 0), has a vertex at (25, 200), goes through (30, 15) and goes through (35, 0).

If the end-of-year analysis indicates that profits did not meet expectations, which inequality in vertex form represents the region containing the results of the year?

y less-than negative 2 (x + 25) squared minus 200
greater-than 2 (x minus 25) squared + 200
y greater-than 2 (x + 25) squared minus 200
y less-than minus 2 (x minus 25) squared + 200

Answer 1

The inequality that represents the region containing the results of the year is y > 2(x + 25)² - 200.

Step-by-step explanation:

The graph represents a parabola with a dashed boundary line opening down, going through points (15, 0), (25, 200), (30, 15), and (35, 0).

To determine the inequality that represents the region containing the results of the year, we need to analyze the graph's vertex and the direction it opens.

Since the vertex is at (25, 200) and the graph opens downwards, the coefficient of the squared term must be negative. This narrows down the options to either y < -2(x + 25)² - 200 or y > 2(x + 25)² - 200.

To determine which inequality is correct, we can analyze the (30, 15) point on the graph.

Substituting the x and y coordinates into the inequalities, we find that the correct inequality is y > 2(x + 25)² - 200.