A rectangle is inscribed between the function y= -x² + 49 and the x-axis.What is the maximum area of the square if the base if two vertices of the square lie on the x-axis? A)3.5 B)257.25 C)428.75 D)8.042 E)40.459

Question

Quizplus · Accepted Answer

The function given is $y = -x^2 + 49$, which is a parabola opening downwards with its vertex at (0, 49). The x-intercepts of the parabola can be found by setting $y = 0$, leading to $x^2 = 49$, or $x = \pm7$. This means the parabola intersects the x-axis at $x = -7$ and $x = 7$, giving a total width of 14 units for the base of the rectangle (which is a square in this case). Since the square's vertices lie on the x-axis and its sides are perpendicular to the x-axis, the side length of the square is also the height of the square. Therefore, the side length of the square is 7 (half of the total width), and the area of the square is $side^2 = 7^2 = 49$. However, the question seems to have a typo in the options provided, as none of the options match the calculated area of 49. Given the options, the closest match or a possible typo could be option B, 257.25, but it doesn't accurately reflect the correct calculation based on the provided function and conditions.

A Rectangle Is Inscribed Between the Function Y= -X2

A Rectangle Is Inscribed Between the Function Y= -X²