︠806dddac-1062-41b6-96b3-81d2a544542bi︠
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<p>EXAMPLE 1&nbsp; Solving a Polynomial Inequality</p>
<p>Solve and graph the solution set on a real number line:&nbsp; $2x^2 + x &gt; 15$.</p>

︡b6436011-f016-4bdb-824a-19b35907a68b︡{"html": "<p>EXAMPLE 1&nbsp; Solving a Polynomial Inequality</p>\n<p>Solve and graph the solution set on a real number line:&nbsp; $2x^2 + x &gt; 15$.</p>"}︡
︠18065841-aa80-448e-8066-53d66e05d04c︠
f(x) = 2*x^2 + x - 15
solve(f(x) == 0, x)
︡810fffeb-8364-442f-95f8-8151ab89a877︡︡
︠67536e47-7e95-4a3f-82f1-5bfcd9346612︠
plot(f, -4, 3)
︡a6ad0101-087d-4abf-ace8-973b5af51731︡︡
︠f17775e7-0550-4a11-b270-5fd67b8fac2ei︠
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<p><a href="http://www.wolframalpha.com/input/?i=2x^2+%2B+x+%3E+15">http://www.wolframalpha.com/input/?i=2x^2+%2B+x+%3E+15</a></p>

<p>EXAMPLE 2&nbsp; Solving a Polynomial Inequality</p>
<p>Solve and graph:&nbsp; $x^3 + x^2 &le; 4x + 4$.</p>

︡52f2c8c3-9e86-4e3b-9e80-be717159919a︡{"html": "<p><a href=\"http://www.wolframalpha.com/input/?i=2x^2+%2B+x+%3E+15\">http://www.wolframalpha.com/input/?i=2x^2+%2B+x+%3E+15</a></p>\n\n<p>EXAMPLE 2&nbsp; Solving a Polynomial Inequality</p>\n<p>Solve and graph:&nbsp; $x^3 + x^2 &le; 4x + 4$.</p>"}︡
︠143f08aa-c34f-448b-a0d8-58cffbe6b37e︠
f(x) = x^3 + x^2 - 4*x - 4
solve(f(x) == 0, x)
︡325d1c28-d626-4fad-82c4-d8065681a93d︡︡
︠5c0fb24e-3cce-40da-8537-d7ed6159b29d︠
plot(f, -3, 3)
︡e8966a68-5a57-4ccf-83f5-6b7f2b114e66︡︡
︠9f1c70e1-37b3-47cb-97eb-07d9910164bci︠
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<p><a href="http://www.wolframalpha.com/input/?i=x^3+%2B+x^2+%E2%89%A4+4x+%2B+4">http://www.wolframalpha.com/input/?i=x^3+%2B+x^2+%E2%89%A4+4x+%2B+4</a></p>

<p>EXAMPLE 3&nbsp; Solving a Rational Inequality</p>
<p>Solve and graph:&nbsp; $\frac{x + 1}{x + 3} &ge; 2$.</p>

︡64e569d0-eb1d-4e52-9c02-1b0341507524︡{"html": "<p><a href=\"http://www.wolframalpha.com/input/?i=x^3+%2B+x^2+%E2%89%A4+4x+%2B+4\">http://www.wolframalpha.com/input/?i=x^3+%2B+x^2+%E2%89%A4+4x+%2B+4</a></p>\n\n<p>EXAMPLE 3&nbsp; Solving a Rational Inequality</p>\n<p>Solve and graph:&nbsp; $\\frac{x + 1}{x + 3} &ge; 2$.</p>"}︡
︠af3675a6-f3ce-403d-948b-ccd03ead5b63︠
f(x) = (x+1)/(x+3) - 2
f
︡e7cb3312-c972-4966-acbf-a62dca56fc19︡︡
︠1553ff1d-7dcf-4d76-814e-1b8243873712︠
plot(f, -6, -2, ymin = -10, ymax = 10)
︡86a7cc2b-88c2-4168-ab5e-3e4ed1f96326︡︡
︠e2a8ba5d-ab15-4c59-8a17-7d534ad64b72︠
f(x) = (-x - 5)/(x + 3)
f
︡3d876d15-b075-4783-bfa0-6ce4b9c37d32︡︡
︠8e08186c-7e66-4587-8bb1-87bad559e652︠
plot(f, -6, 2, ymin = -10, ymax = 10)
︡af4b9b1b-300a-4a63-9ccc-c376ed65a57e︡︡
︠85065e2e-21e3-46c1-ab82-b56fdcdfaf5ei︠
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<p><a href="http://www.wolframalpha.com/input/?i=%28x%2B1%29%2F%28x%2B3%29%3E%3D2">http://www.wolframalpha.com/input/?i=%28x%2B1%29%2F%28x%2B3%29%3E%3D2</a></p>

<p>EXAMPLE 4&nbsp; Using the Position Function $s(t) = -16t^2 + v_0t + s_0$</p>
<p>If the initial height $s_0 = 190$ and the initial velocity $v_0 = 96$ feet per second, during what times will the height $s(t) &gt; 190$?</p>

︡3f871b20-3394-463b-8c8e-f70920b5fdbd︡{"html": "<p><a href=\"http://www.wolframalpha.com/input/?i=%28x%2B1%29%2F%28x%2B3%29%3E%3D2\">http://www.wolframalpha.com/input/?i=%28x%2B1%29%2F%28x%2B3%29%3E%3D2</a></p>\n\n<p>EXAMPLE 4&nbsp; Using the Position Function $s(t) = -16t^2 + v_0t + s_0$</p>\n<p>If the initial height $s_0 = 190$ and the initial velocity $v_0 = 96$ feet per second, during what times will the height $s(t) &gt; 190$?</p>"}︡
︠7d71dcdf-7279-4d54-889b-08bf7d16ed77︠
s(t) = -16*t^2 + 96*t + 190
︡0f665a92-f450-4e05-b477-c69b37c57582︡︡
︠e033af93-355b-40e7-8d6b-6091da1905b1︠
solve(s(t) == 190, t)
︡22a2bdaf-be06-45ec-8196-06ba00154954︡︡
︠283ba205-902c-4ea5-9c8f-efeb51d31f92︠
h(t) = 190
plot(s, 0, 8) + plot(h, 0, 8)
︡00c5fe97-6941-4a73-9078-ae6983acbe5c︡︡