Asked by j

A pattern of rectangles is formed by decreasing the length and increasing the width, each by the same amount. The relationship between x, the amount of increase, and A, the area of the rectangle represented by the increase, is quadratic.

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
Choose the graph that rises then falls (the one that increases from 0 to 3 and then decreases from 3 to 9).

Reason: A(x) = (L − x)(W + x) = −x^2 + (L − W)x + LW is a quadratic with negative x^2, so its parabola opens downward — area increases to a maximum and then decreases.