Math Problem Solver

The diagram shows a shaded region containing coordinates $(x,y)$ that make what inequality true?

Write your answer in the form $y~\boxed{\phantom{bl}}~ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers, and the box is an inequality symbol. Use "<=" for $\leq$ or ">=" for $\geq$. Sample answer: $y >= x^2 - 2x + 3$. Note that these are not the correct numbers to use, just the format of the answer.

[asy]

import graph; size(7cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-1.3,xmax=5.7,ymin=-3.56,ymax=3.58; real f1(real x){return (1-x)*(x-4);}

filldraw(graph(f1,-1.29,5.69)--cycle,rgb(0.8,0.8,0.8),linewidth(1.2));

Label laxis; laxis.p=fontsize(10);

xaxis("$x$",xmin,xmax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true); yaxis("$y$",ymin,ymax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true); dot((4,0),ds); dot((1,0),ds);

dot((5/2, 9/4),ds);

label("$\left(\frac{5}{2}, \frac{9}{4}\right)$", (5/2, 9/4), N, p=fontsize(10pt));

clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]