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The diagram shows a shaded region containing coordinates  that make what inequality true?

Write your answer in the form , where , , and  are real numbers, and the box is an inequality symbol. Use "<=" for  or ">=" for . Sample answer: . 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]Your Answer

 Oct 2, 2022
 #1
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The solution is y <= 2x^2 - 6x - 7.

 Oct 8, 2022

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