Task 827
Task 827: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. Square $ABCD$ is inscribed in the region bound by the parabola $y = x^2 - 8x + 12$ and the $x$-axis, as shown below. Find the area of square $ABCD.$ asy unitsize(0.8 cm); real parab (real x) {…
The task
Square $ABCD$ is inscribed in the region bound by the parabola $y = x^2 - 8x + 12$ and the $x$-axis, as shown below. Find the area of square $ABCD.$ [asy] unitsize(0.8 cm); real parab (real x) { return(x^2 - 8*x + 12); } pair A, B, C, D; real x = -1 + sqrt(5); A = (4 - x,0); B = (4 + x,0); C = (4 + x,-2*x); D = (4 - x,-2*x); draw(graph(parab,1.5,6.5)); draw(A--D--C--B); draw((1,0)--(7,0)); label("$A$", A, N); label("$B$", B, N); label("$C$", C, SE); label("$D$", D, SW); [/asy]