4.16 Quadratic inequalities

The following graph shows the temperature throughout the month of March. Actually, I just made this graph up—the numbers do not actually reflect the temperature throughout the month of March. We’re just pretending, OK?

• a On what days was the temperature exactly $0^{°}$ C?
• b On what days was the temperature below freezing?
• c On what days was the temperature above freezing?
• d What is the domain of this graph?
• e During what time periods was the temperature going up?
• f During what time periods was the temperature going down?

The following graph represents the graph $y=f(x)$ .

• a Is it a function? Why or why not?
• b What are the zeros?
• c For what $x$ -values is it positive?
• d For what $x$ -values is it negative?
• e Draw the graph $y=f(x)-2$ .
• f Draw the graph $y=-f(x)$

$x^2+\mathrm{8x}+\text{15}>0$

• a Draw a quick sketch of the graph by finding the zeros, and noting whether the function opens up or down.
• b Now, the inequality asks when that function is> $0$ —that is, when it is positive. Based on your graph, for what $x$ -values is the function positive?
• c Based on your answer to part (b), 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 flying fish jumps from the surface of the water with an initial speed of 4 feet/sec.

• a Write the equation of motion for this fish.
• b Find the zeros of the graph, and graph it.
• c Based on your graph, answer the question: during what time interval was the fish above the water?
• d During what time interval was the fish below the water?
• e At what time(s) was the fish exactly at the level of the water?
• f What is the maximum height the fish reached in its jump?