Exam 2: Linear and Quadratic Functions

Solve the problem. -Let f(x) be the function represented by the dashed line and g(x) be the function represented by the solid line. Solve the equation f(x) $f ( x ) \geq g ( x )$ A) $x \geq - 1$ B) $x \leq 2$ C) $x < - 1$ D) $x \geq 2$

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = x ^ { 2 } - 6 x$

Solve the inequality. Express your answer using interval notation. Graph the solution set. - $| 8 x | > 16$

Determine the domain and the range of the function. - $f ( x ) = x ^ { 2 } + 8 x + 7$

Find the zeros of the quadratic function by completing the square. List the x-intercepts of the graph of the function. - $f ( x ) = x ^ { 2 } - 14 x + 24$

Match the graph to one of the listed functions. -

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = - 4 x ^ { 2 } + 8 x$

Find the zero of the linear function. -f(x) = x + 7

Use a graphing calculator to plot the data and find the quadratic function of best fit. -A rock is dropped from a tall building and its distance (in feet) below the point of release is recorded as accurately as possible at various times after the moment of release. The results are shown in the table. Find the regression equation Of the best model. (seconds after release) 2 2 3 4 5 6 (distance in feet) 16 63 146 255 403 572

Find the complex zeros of the quadratic function. - $f ( x ) = x ^ { 2 } - 36$

Determine where the function is increasing and where it is decreasing. - $f ( x ) = - x ^ { 2 } + 2 x + 8$

Solve the problem. -The following scatter diagram shows heights (in inches) of children and their ages. $\text { Height (inches) }$ Age (years) What happens to height as age increases?

Solve the problem. -The profit that the vendor makes per day by selling x pretzels is given by the function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 350$ Find the number of pretzels that must be sold to maximize profit.

Solve the problem. -A suspension bridge has twin towers that are 1300 feet apart. Each tower extends 180 feet above the road surface. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cable at a point 200 feet from the center of the bridge.

Solve the problem. -The quadratic function $f ( x ) = 0.0040 x ^ { 2 } - 0.43 x + 36.98$ models the median, or average, age, y, at which U.S. men were first married x years after 1900. In which year was this average age at a minimum? (Round to the nearest Year.) What was the average age at first marriage for that year? (Round to the nearest tenth.)

Use factoring to find the zeros of the quadratic function. List the x-intercepts of the graph of the function. - $f ( x ) = 3 x ^ { 2 } - 4 x - 7$

Graph the function using its vertex, axis of symmetry, and intercepts. - $f(x)=-x^{2}+8 x-7$ A) vertex $( 4 , - 9 )$ intercepts $( 7,0 ) , ( 1,0 ) , ( 0,7 )$ B) vertex $( 4,9 )$ intercepts $( 7,0 ) , ( 1,0 ) , ( 0 , - 7 )$ C) vertex $( - 4 , - 9 )$ intercepts $( - 7,0 ) , ( - 1,0 ) , ( 0,7 )$ D) vertex $( - 4,9 )$ intercepts $( - 7,0 ) , ( - 1,0 ) , ( 0 , - 7 )$

Solve the equation. - $\left| x ^ { 2 } + 7 x + 10 \right| = 0$

Plot and interpret the appropriate scatter diagram. -The one-day temperatures for 12 world cities along with their latitudes are shown in the table below. Make a scatter diagram for the data. Describe what happens to the one-day temperatures as the latitude increases. City Temperature (F) Latitude Oslo, Norway 3 5 Seattle, WA 5 4 Anchorage, AK 4 6 Paris, France 6 4 Vancouver, Canada 5 4 London, England 4 5 Tokyo, Japan 5 3 Cairo, Egypt 8 3 Mexico City, Mexicp 8 1 Miami, FL 8 2 New Delhi, India 9 2 Manila, Philippines 9 1 Latitude (degrees) Temperature (F)°

Use factoring to find the zeros of the quadratic function. List the x-intercepts of the graph of the function. - $g ( x ) = x ^ { 2 } - 2 x - 15$