Quadratic equations Questions and Answers

The graph of a quadratic function with vertex 1 3 is shown in the figure below Find the domain and the range 1017 10 2 10 Write the domain and range using interval notation

6 5 4 3 2 1 5 4 3 2 1 y N 3 4 5 6 1 2 34 5 Write an equation for the function graphed above

Given a temperature of 45 C find the equivalent in F 45 C F If necessary round to two decimal places

stim J9 ton 4 2009 9 Given that the graph of the function y f x is shown below left graph the indicated transformed function on the right Clearly indicate the order in which you applied the transformations 5y aks a y f x y 2f x 4 clown b y f x c y f x Y 9 5 y f 2 x 3 22 4 y f x 2 3 5 compress

Graph the derivative of the function graphed on the right Choose the correct graph below DA a OB a OC Nia OD W o t

Find an equation for the elipse whose vertices are at 7 4 and 3 4 and focus is at 1 4 Graph the equation The equation of the ellipse is 1 COCX

Which of the following graphs show a function which is one to one Select all correct answers Select all that apply 0 A

A cow is tethered to one comer of a square barn 8 feet by 8 feet with a rope 100 feet long See the illustration to the right What is the maximum grazing area for the cow The maximum grazing area is approximately square feet 8 Rope AAAAAAA 8 Ba

Solve and graph the solution set x 8 5 or x 8 6

4 cot sin 20 and 15 and terminates in Quadrant III 8 11 tan give

F Verify the identity cos A 2 sin A 1 cos A 1

The graph shown is a horizontal stretch or compression of the graph of y sin z 3 2JT I 2 The equation of the graph shown is y J 2pt 3j Enter a sine function

The percentages of the people of a certain country who went to the movies at least once in the past year are shown in the table for various age groups Let p f a be the percentage of people at age a years who go to the movies Complete parts a through e Q Q M O B O C Age Group years 18 24 25 39 Q 40 49 50 59 over 60 a Use a graphing calculator to draw a scatterplot of the data Choose the correct graph below The scatterplots are graphed using a window 16 70 5 by 36 96 10 O A O D Age Used to Represent Age Group years 21 0 32 0 44 5 54 5 65 0 Q Q Percent 91 78 M 68 51 41 O

The functions f and g are defined by the following tables Use the tables to evaluate the given composite function gof 4 gof 4 X 4 0 1 3 f x 1 4 5 1 4 1 4 8 g x 0 4 2 1

G x 3x 15x 18x describe the left hand behavior A C B None of these D E 81118 F f x 00 818 f x 8 18 f x 00 X 0 f x 81118 f x

1 point Consider the function Give the domain of the function f z in interval notation Domain Give the range of the function f z in interval notation Range f x log 13 3z 4

y a Eliminate the parameter to find a Cartesian equation of the curve b Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases y y Need Help edit 0 5 0 5 0 4 0 6 0 8 Frot toj 0 8 0 6 0 4 0 2 0 5 0 3 1 0 0 5 0 5 02 0 4 06 0 8 0 8 as 0 4 0 2 0 5

Plot in the complex plane Z 2 2 i

2 Modeling the population of a fishery helps to determine the number of fish that can be harvested from the population without affecting long term sustainability A certain large pond is stocked with 140 fish and a fisheries expert has determined that the population can be modeled by the formula P 3t 6 t 140 where t is the number of days since the fish were introduced to the pond How many days will it take for the fish population to reach 500 Label your answer Hint Recall that t t 2 functi

Evaluate the function for values of x that approach 1 from the left and from the right 5 lim f x X 1 f x lim f x X 1 3 x 1

Let u 2 3 4 v 3 a 6 w 0 4 3 a 3 marks Find the value s of a such that u and are orthogonal b 3 marks Find the value s of a such that and w are parallel c 5 marks Find a vector r of norm 2 in the opposite direction to ux vec

Here is a graph of y f x 8 D 6 5 4 3 2 1 4 3 2 1 2 2 3 N 5 A formula of the form A sin kx C or A cos kx C for f x is f x on 3

Use the graph off at the night to complete each of the parts a through h The domain of fis Type your answer in interval notation b Find the range of f The range of fis Type your answer in interval notation c Find f 4 4 d Find the values of x for which f x 5 The values of x are 0 Use a comma to separate answers as needed e Find the points where the graph of f crosses the x axis The points are Type ordered pairs Use a comma to separate answers as needed f Find the point where the graph of f crosses the y axis The point is Type an ordered pair g Find values of x for which f x 0 The values of x are Type your answer in interval notation h Is f 8 positive or negative O positive CEEDS 42 2 10 B 6

The pH scale for acidity is defined by pH log H where H is the concentration of hydrogen ions measured in moles per liter M a A sample of Pepsi is found to have a hydrogen concentration of 0 00126 M What is the pH pH b The pH of a sample of rhubarb is 3 4 What is the hydrogen concentration x

a en that coOS 4 sin sin B and both angles terminate in quadrant IV find

Solve the inequality f x 20 where f x x 2 x 1 2 by using the graph of the function 30 20 10 10 20 30 40 Q SELES The solution set for f x 20 is Type your answer in interval notation

Given that SQ bisects PSR and PS SR which of the following prove that A PQSARQS P S Q R

10 3 If cos A and A terminates in Quadrant IV use one of the Pythagorean identities 10 to help you determine the value of csc A Then provide a check of your work by building the appropriate triangle

ovide your answer below 7 6 5 4 3 2 65 6 21 FI N W A 5 6 ITE 9 1 2 3 5 6 7

The table below gives for the value of continuous function f at each z value Using the Intermediate Value Theorem and the information in the table determine the smallest interval in which the function must have a root z f x 5 9 25 4 8 03 3 7 05 2 7 01 1 1 02 0 0 69 1 2 43 2 5 45 3 0 76 4 4 93

Find the equation of the quadratic function g whose graph is shown below 10 5 4 2 5 g x

Brooke rides a Ferris wheel for one full rotation Brooke s height above the center of the Ferris wheel in feet h is a function of the number of minutes t since the ride started We will call this function f so that f t h The graph of f is shown below 25 30 20 10 h fit 0 5 a Evaluate 0 5 f 0 5 This value represents a number of Select an answer b Solve f t Preview Preview 15 5 for t If there is more than one answer enter your answers as a comma separated list This value represents a number of Select an answer f

The graph below is a polynomial function in the form f z x a a b x c Find suitable unique real numbers a b and c that describe the graph

Evaluate the function f x x 6 2 at the given values of the independent variable and simplify a f 6 b f 58 c f x 6 a f 6 Simplify your answer b f 58 Simplify your answer c f x 6 Simplify your answer COCOS

Homework HW 3 2 The graph of two functions f and g is illustrated below Use the graph to answer parts a through f 18 36 14 132 94 316 226 40 B Part 5 of 6 Vi points a f g 1 6 Simplify your answer b f g 3 0 Simplify your answer c f g 5 6 Simplify your answer d g f 5 6 Simplify your answer e f g 1 4 Simplify your answer Points 0 of 0 More

The table displays the number of doctors and nurses working in the US Years after 2000 US Doctors US Nurses 0 1 2 5 7 8 9 693345 708463 72034 780662 800586 816727 822016 2271340 2249440 2262020 2421000 2417150 2468340 2542760 Determine the quadratic regression model of the data for US nurses Oy 1174 6x 16536 7x 2273430 Oy 1894 6x 19536 3x 2281912 Oy 1276 3x 15566 5x 2281020 Oy 1272 2x 18538 5x 2271518 2 N O There is no correct answer

State the range of the function in interval notation If necessary use inf for and capital U for union as in inf 9 U 10 inf means 00 9 U 10 00 Do not enter any spaces in the answer f x 17 The range of fis 17 70

Write the equations of the asymptotes of the graph of the function f x 10 50 Do not enter any spaces in the answers The horizontal asymptote is The vertical asymptote is N

Set up a double integral that represents the area of the surface given by z f x y that lies above the region f x y exy R x y 0 x 12 0 y 17 dy dx

19 Solve the following equations for x where x 0 21 a sin x 1 c 4 sin x 2 0 e tan x 1 b cos x 2 22 d sec x 2 f sin 2x

Simplify the expression without using a calculator 10log x

Evaluate the expression without using a calculator In e 8

Evaluate the expression without using a calculator 1 2 log 27 log 2 1 11

Complete the statement about the function If necessary use inf for as in inf means 1 z 50 As y f x 25

Evaluate the following expression without using a calculato 4log 48 log 18

Determine 0 in decimal degrees 0 0 90 Round results to an appropriate number of significant digits sec 0 5 1 A 79 OB 78 7 OC 78 2 D 78

Find the solution set 7 Use to enter fractions as in 34 9 means Do not enter any spaces in the answer 34

Evaluate the following expression without using a calculator log 33

Find the measure of each angle in the triangle What is the measure of angle A STTR GEITEN 2x106 7 14 This figure is not to scale

Evaluate the expression without using a calculator 10log 8