Exam 3: Quadratic, Piecewise-Defined, and Power Functions

Find a power function that models the data in the table. Round to three decimal places if necessary. -A ball is tossed upward. Its height after t seconds is given in the table. Time (seconds) 0.5 1 1.5 2 2.5 Height (feet) 26.5 39.5 44.5 41.5 30.5 Find a quadratic function to model the data. Use the model to determine when the ball reaches its maximum height, as well as the value of the maximum height.

Determine if the vertex of the graph is a maximum point or a minimum point. - $y = 4 ( x + 2 ) ^ { 2 } + 3$

Use the square root method to - $- 3 k ^ { 2 } - 19 = - 94$

Find the exact solutions to the quadratic equation in the complex numbers. - $x ^ { 2 } + x + 6 = 0$

Solve the equation. - $| t - 9 | = 0$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=x^{2}-2 x-8$

Provide an appropriate response. -Suppose you have to develop a model to predict snowfall for the upcoming winter based on data from previous winters. Consider the table of annual snowfall over the last five years: Snowfall (y) (in inches) 180 168 163 155 165 year (x) 1 2 3 4 5 Would it be possible to come up with one model that predicted very low amounts of snowfall and another that predicted very high amounts of snowfall? How so? If you were employed by a ski resort to come up with a model, what type of model would you use? What could be done to try to reduce the chance of coming up with such different models?

Determine if the function is concave up or concave down in the first quadrant. - $y = x ^ { 0.8 }$

Determine if the function is concave up or concave down in the first quadrant. - $y = x ^ { 5.4 }$

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. - -4 0 7 -8 12 -17

Provide an appropriate response. -Which one of the following methods cannot be used to solve the equation $x ^ { 2 } - 4 x - 6 = 0$

The number of people present at a stadium holding a big rock concert can be estimated with the following function: $y = 13252 x x ^ { 0.73 } + 0.51 x + 102$ where y is the number of people present and x is the amount of time after 3:00 P.M. on the day of the concert. Predict the number of people present at 7:00PM.

Determine if the graph of the function is concave up or concave down - $y = - x ^ { 2 } + 1$

Provide an appropriate response. -Write the equation of the quadratic function whose graph is shown.

Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let $\mathrm { L } ( \mathrm { x } )$ be the cost of mailing a letter weighing $x$ ounces. Graph $y = \mathrm { L } ( \mathrm { x } )$ .

Solve the equation. - $\left| \frac { 1 } { 4 } x - 6 \right| = 4$

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph? - $f(x)=-4 x^{2}+2 x-1$

At Allied Electronics, production has begun on the X-15 Computer Chip. The total revenue function is given by $R ( x ) = 48 x - 0.3 x ^ { 2 }$ and the total profit function is given by $P ( x ) = - 0.3 x ^ { 2 } + 42 x - 10$ where x represents the number of boxes of computer chips produced. The total cost function, C(x) , is such that C(x)=R(x)-P(x) . Find C(x) .

Find a power function that models the data in the table. Round to three decimal places if necessary. -The percent of people who say they plan to stay in the same job position until they retire has decreased over recent years, as shown in the table below. Year 2005 2006 2007 2008 2009 2010 Percent 42 38 35 34 30 26 Find a power function that models the data in the table using an input equal to the number of years from 2000. According to the unrounded model, what percent of people will plan to stay in the same job position until retirement in 2014?

You are given a graph of a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ for different values of $a , b$ , and $c$ . For this function, a. Determine whether the discriminant is positive, negative, or zero. b. Determine if there are 0,1 , or 2 real solutions to $f ( x ) = 0$ . c. Solve the equation $f ( x ) = 0$ . -A ball is thrown downward from a window in a tall building. The distance traveled by the ball in t seconds is $\mathrm { s } = 16 \mathrm { t } ^ { 2 } + 32 \mathrm { t }$ where s is in feet. How long (to the nearest tenth) will it take the ball to fall 230 feet?