Question

Select the point that satisfies y ≤ x2 - 5x + 6.

A. (1,1)

B. (4,4)

C. (2,2)

D. (3,3)

Answer 1

`y\leqx^2-5x+6\\\\A.\ (1,\ 1)\to x=1;\ y=1\\\\\text{substitute}\\\\1\leq1^2-5\cdot1+6\\1\leq1-5+6\\1\leq2\ \boxed{TRUE}\\\\B.\ (4,\ 4)\to x=4;\ y=4\\\\\text{substitute}\\\\4\leq4^2-5\cdot4+6\\4\leq16-20+6\\4\leq2\ \boxed{FALSE}\\\\C.\ (2;\ 2)\to x=2;\ y=2\\\\\text{substitute}\\\\2\leq2^2-5\cdot2+6\\2\leq4-10+6\\2\leq0\ \boxed{FALSE}\\\\D.\ (3;\ 3)\to x=3;\ y=3\\\\\text{substitute}\\\\3\leq3^2-5\cdot3+6\\3\leq9-15+6\\3\leq0\ \boxed{FALSE}\\\\\text{Answer:}\ A.\ (1,\ 1)`