# MATH / 

task_id: fc97ac86-3036-5fb6-8002-5f80ecc5d188
task_key: intermediate~5falgebra--test--fc97ac86-3036-5fb6-8002-5f80ecc5d188
task_revision_id: 1

{"level":"Level 5","problem":"The graph of $y = \\frac{p(x)}{q(x)}$ is shown below, where $p(x)$ and $q(x)$ are quadratic.  (Assume that the grid lines are at integers.)\n\n[asy]\nunitsize(0.6 cm);\n\nreal func (real x) {\n  return (-(x + 5)*(x - 4)/(x - 2)^2);\n}\n\nint i;\n\nfor (i = -8; i <= 8; ++i) {\n  draw((i,-8)--(i,8),gray(0.7));\n  draw((-8,i)--(8,i),gray(0.7));\n}\n\ndraw((-8,0)--(8,0));\ndraw((0,-8)--(0,8));\ndraw((2,-8)--(2,8),dashed);\ndraw((-8,-1)--(8,-1),dashed);\ndraw(graph(func,-8,1.9),red);\ndraw(graph(func,2.1,8),red);\n\nlimits((-8,-8),(8,8),Crop);\n[/asy]\n\nThe horizontal asymptote is $y = -1,$ and the only vertical asymptote is $x = 2.$  Find $\\frac{p(-1)}{q(-1)}.$","type":"Intermediate Algebra"}

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