Exam 2: Linear and Quadratic Functions

Graph the function using its vertex, axis of symmetry, and intercepts. - $f(x)=x^{2}+4 x+3$ A) vertex $( - 2,1 )$ intercepts $( - 1,0 ) , ( - 3,0 ) , ( 0 , - 3 )$ B) vertex $( 2,1 )$ intercepts $( 1,0 ) , ( 3,0 ) , ( 0 , - 3 )$ C) vertex $( - 2 , - 1 )$ intercepts $( - 1,0 ) , ( - 3,0 ) , ( 0,3 )$ D) vertex $( 2 , - 1 )$ intercepts $( 1,0 ) , ( 3,0 ) , ( 0,3 )$

Determine the domain and the range of the function. - $f ( x ) = - 4 x ^ { 2 } - 2 x - 8$

Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. - $f ( x ) = 3 x ^ { 2 } + 2 x - 6$

Determine if the type of relation is linear, nonlinear, or none. -

Solve f(x) = g(x). Find the points of intersection of the graphs of the two functions. - f(x)=7x+8 g(x)=

Determine the average rate of change for the function. - $h ( x ) = - \frac { 3 } { 4 } x - 3$

Without solving, determine the character of the solutions of the equation. - $x ^ { 2 } - 6 x + 5 = 0$

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. - 3 5 7 15 16 8 11 7 14 20

Solve f(x) = g(x). Find the points of intersection of the graphs of the two functions. - f(x)=-13x+36 g(x)=2-16x+32 A) x=-,x= B) $x = 4 , x = - 1$ C) $x = \frac { 1 } { 4 } , x = - 1$ D) $x = - \frac { \sqrt { 17 } } { 2 } , x = \frac { \sqrt { 17 } } { 2 }$

Use a graphing calculator to plot the data and find the quadratic function of best fit. -Southern Granite and Marble sells granite and marble by the square yard. One of its granite patterns is price sensitive. If the price is too low, customers perceive that it has less quality. If the price is too high, customers Perceive that it is overpriced. The company conducted a pricing test with potential customers. The following Data was collected. Use a graphing calculator to plot the data. What is the quadratic function of best fit? Price, x Buyers, B \ 20 30 \ 30 50 \ 40 65 \ 60 75 \ 80 72 \ 100 50 \ 110 25

Find the real zeros of the function. List the x-intercepts of the graph of the function. - $F ( x ) = x ^ { 4 } - 10 x ^ { 2 } + 9$

Determine where the function is increasing and where it is decreasing. - $g ( x ) = 6 x ^ { 2 } + 120 x + 564$

Solve the problem. -The following data represents the number of employees at a company at the start of each year since the company began. month 1 2 3 4 5 6 7 number 3 172 403 571 823 1061 1194 Find the slope of the line of best fit for the data set and interpret it.

Determine if the type of relation is linear, nonlinear, or none. -

Determine the average rate of change for the function. -f(x) = 5x - 3

Solve the problem. -The revenue achieved by selling $x$ graphing calculators is figured to be $x ( 28 - 0.2 x )$ dollars. The cost of each calculator is $\$ 20$ . How many graphing calculators must be sold to make a profit (revenue - cost) of at least $\$ 75.00 ?$

Without solving, determine the character of the solutions of the equation. - $f ( x ) = x ^ { 2 } + 3 x - 7$

Determine the domain and the range of the function. - $f ( x ) = x ^ { 2 } - 2 x - 8$

Solve the problem. -The manufacturer of a CD player has found that the revenue R (in dollars) is $R ( p ) = - 5 p ^ { 2 } + 1,460 p$ when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?

Solve the problem. -A rock falls from a tower that is 208 ft high. As it is falling, its height is given by the formula $h = 208 - 16 t ^ { 2 }$ How many seconds will it take for the rock to hit the ground (h=0)?