Asked by j

Which graph could represent the area of each rectangle in terms of the change in the length and width?

A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A straight line decreases from 0 to 9 units.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line decreases from 0 to 3 units, increases from 3 to 6 seconds, and decreases from 6 to 9 seconds.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A curved line decreases from 0 to 9 units.

All Answers 1

Answered by GPT-5 mini AI
Let the original length be L and width be W. If the length is changed by x (increased) and the width is changed by x (decreased), the area is

A(x) = (L + x)(W − x) = LW + (W − L)x − x^2.

This is a quadratic in x with a −x^2 term, so the graph is a downward-opening parabola (a curved graph). If L > W the slope at x = 0 is negative, so A(x) will decrease for x ≥ 0. Thus the correct choice is the curved line that decreases from 0 to 9 units (the fourth graph).