4.18 Sample test: quadratics ii

$x=-{\mathrm{3y}}^2+5$

• A

  Opens (up / down / left / right)

• B

  Vertex: ___________

• C

  Sketch a quick graph on the graph paper

$y+9={\mathrm{2x}}^2+\mathrm{8x}+8$

• A

  Put into the standard form of a parabola.

• B

  Opens (up / down / left / right)

• C

  Vertex: ___________

• D

  Sketch a quick graph on the graph paper

For what $x$ -values is this inequality true?

For what $x$ -values is this inequality true?

A rock is thrown up from an initial height of 4' with an initial velocity of 32 ft/sec. As I’m sure you recall, $h(t)=h_o+v_{o}t-\text{16}{t}^2$ .

• A

  Write the equation of motion for the rock.

• B

  At what time (how many seconds after it is thrown) does the rock reach its peak? How high is that peak? (Don’t forget to answer both questions…)

• C

  During what time period is the rock above ground ?

A hot dog maker sells hot dogs for $2 each. (So if he sells $x$ hot dogs, his revenue is $\mathrm{2x}$ .) His cost for manufacturing $x$ hot dogs is $\text{100}+\frac{1}{2}x+\frac{1}{\text{1000}}{x}^2$ . (Which I just made up.)

• A

  Profit is revenue minus cost . Write a function $P(x)$ that gives the profit he will make, as a function of the number of hot dogs he makes and sells.

• B

  How many hot dogs should he make in order to maximize his profits? What is the maximum profit?

• C

  How many hot dogs does he need to make, in order to make any profit at all? (The answer will be in the form“as long as he makes more than this and less than that or, in other words, between this and that , he will make a profit.”)