4.17 Homework: quadratic inequalities

$x^2+\mathrm{8x}+7>\mathrm{2x}+3$

• a Collect all the terms on one side, so the other side of the inequality is zero. Then graph the function by finding the zeros.
• b Based on your graph, for what $x$ -values is this inequality true?
• c Based on your answer, choose one $x$ -value for which the inequality should hold, and one for which it should not. Check to make sure they both do what they should.

• a Graph
• b Based on your graph, for what $x$ -values is this inequality true?
• c Based on your answer, choose one $x$ -value for which the inequality should hold, and one for which it should not . Check to make sure they both do what they should.

$-{\mathrm{2x}}^2+\mathrm{8x}>9$

• a Collect terms and graph
• b Based on your graph, for what $x$ -values is this inequality true?
• c Based on your answer, choose one $x$ -value for which the inequality should hold, and one for which it should not. Check to make sure they both do what they should.

$-x^2+\mathrm{4x}+3>0$

• a Graph the function
• b Based on your graph, for what $x$ -values is this inequality true?
• c Based on your answer, choose one $x$ -value for which the inequality should hold, and one for which it should not. Check to make sure they both do what they should.

$x^2>x$

• a Collect terms and graph
• b Based on your graph, for what $x$ -values is this inequality true?
• c Now, let’s solve the original equation a different way—divide both sides by $x$ . Did you get the same answer this way? If not, which one is correct? (Answer by trying points.) What went wrong with the other one?

• a For what values of $c$ will this inequality be true in some range ?
• b For what values of $c$ will this inequality never be true?
• c For what values of $c$ will this inequality always be true?