Quadratic equations Questions and Answers

1 The parent function for each function below is y x Graph the parent function and each function below on a separate piece of paper take a picture and upload Do not use a graphing utility show use of transformations by sketching the parent graph and then translate a y x 2 b y x 1 c y 3 x 1 4

3 The point P 5 2 4 Determine D 18 C

3 A sprinkler can water between 1 and 130 square yards of a lawn The length L in inches of rotating pipe needed to water A square yards is given by the function L 117 75 A Graph the equation on a calculator How much area can be watered if the length of the pipe is 500 or 1300 inches long Give a reason for your answers

Find the domain and the range of the relation shown in the given graph Also determine whether the relation is a function Next question

4 A desktop world globe has a volume of about 1396 cubic inches The radius of Earth is approximately equal to the radius of the globe raise 4 r to the 10th power Find the radius of the earth Hint you will need to use the formula for the volume of a sphere V

An athlete whose event is the shot put releases a shot When the shot whose path is shown by the graph to the right is released at an angle of 40 its height f x in feet can be modeled by f x 0 01x 0 8x 6 3 where x is the shot s horizontal distance in feet from its point of release Use this model to solve parts a through c and verify your answers using the graph a What is the maximum height of the shot and how far from its point of release does this occur The maximum height is 22 3 which occurs 40 feet from the point of release Type an integer or decimal rounded to four decimal places as needed b What is the shot s maximum horizontal distance to the nearest tenth of a foot or the distance of the throw 87 2 feet Type an integer or decimal rounded to the nearest tenth as needed c From what height was the shot released feet Shot Put s Height A 50 40 30 20 10 0 0 20 40 60 80 100 Shot Put s Horizontal Distance

19 Re write the following without trigonometric functions You may assume that x 20 x 1 coticos

Non graphing calculators may be used on this assessment Here is a graph of y a x represented with a solid curve and a set of data b x represented by the dots on the graph 1 b Write an expression for the Data set function b x in terms of a x

Use the vertex and intercepts to sketch the graph of the quadratic function Give the equation of the parabola s axis of symmetry Use the graph to determine the domain and range of the function f x 4x x 12 Use the graphing tool to graph the equation Use the vertex and one of the intercepts to draw the graph The axis of symmetry is x 2 Type an equation The domain of the function is Type your answer in interval notation 10 8 18 16 14 12 to Ay 6 14 2 2 4 6 18 to X 8 10

Example Let f x x4 3 Q x Find Qf and Qf Q

The pitch of a roof is its slope Find the pitch of the of the roof shown

raw the following triangle after a translation 3 units to the left and 4 units down 3 1

Trigonometric functions are written in general form according to the equations below where the variable a is called the AMPLITUDE f x a sin b x h k f x a cos b x h k Match the following trig functions to their corresponding graphs f x 2 sin x f x 3 cos x f x 3 cos x f x 2 sin x a b C d 2 2021 2 7 2 34 3 AA J 23 2 2 57 2 2 34 2 3 2 25 2 12 32 2 5 7 2 W AA 3 2 2 5702 Q

Select one a O y 4 5 Oy 5 2 O y 2 5 nction is represented in the table O y 5 4 1 0 1 2 0 03125 0 125 0 5 2 8

Choose the graph and the solution for X 0 125 2 5 4 x

Given the graph below with vertical asymptotes at x 2 and x 4 solve 2 3 x 2 1 Be sure to use correct notation x 4 24 Q mo hp 3 1 H 8 1

7 2 1 6 12 0 8 0 4 00 8 1 32 atm 1 O atm 16 0 atm O 1 atm 24 Based on the information in the graph what is the water pressure at sea level 32 d

L 96 8 7 6 54 4 3 du 2 14 www fut 2 3 87 58 8 9 X Which equation represents the data in the graph O y x 8x 16 O y 5 5x 0 5x 4 Oy x 4x 4 O y 25x2 0 5x 4

A travel agency made the table below to represent the profits it makes on a certain vacation package Number of People vs Profit Number of People Who Buy the Package x 10 20 30 40 50 Profit per Person in dollars y 500 800 900 800 500 Which of the following explains the best model for the data in the table O an absolute value function since the values increase and then decrease an exponential function since the ratios of the y values are about the same a linear function since the profit per person changes by 30 for each additional person a quadratic function since the points lie on a curve that is symmetric about the line x 30

The test scores of 10 students are listed below Find the value of the third quartile 67 67 69 70 70 74 75 78 79 79 80 OA 69 OB 78 5 C 78 OD 79

10height 9 8 00 7 6 5 4 3 2 1 4 8 Br doen WARUM S 73 12 Distance Which type of function models the data on the graph O inverse variation O linear O square root O quadratic

For the following data approximate the mean miles per day Miles per day Frequency 1 2 3 4 5 6 7 8 9 10 OA 5 B 10 OC 4 OD 2 9 22 28 15 4

In the figure triangle ABC is a right triangle CQ 8 and BQ 4 Also ZAQC 30 and ZCQB 45 Find the length of AQ Hint First use the Law of Cosines to find expressions for a b and c C b A O C X B 30 45 Q

Joolz James McCray Attempt 1 Which of the following graphs represents an odd function with exactly one real zero and a positive leading coefficient

1 point Jerry drives 14 miles per hour slower than Subin They started at the same spot and drove in opposite directions After 5 3 hours they were 466 4 miles apart Find each car s speed Jerry drives at a speed of hour Subin drives at a speed of per hour miles per miles

1 point Find the slope and the equation for the line passing through the point 1 3 4 with y intercept at y 1 a m b The equation for the line in slope intercept form

ind the volume of the solid generated by revolving the region bounded by the given equations about the y axis y3 2 x 0 and y 7

State the open intervals over which the function is a increasing b decreasing and c constant 10 3 0 Ay 10 k 37 8 7 a Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is increasing over the open interval s Type your answer in interval notation Use a comma to separate answers as needed OB The function is never increasing b Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is decreasing over the open interval s Type your answer in interval notation Use a comma to separate answers as needed B The function is never decreasing c Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is constant over the open interval s Type your answer in interval notation Use a comma to separate answers as needed

Graph the following linear function Give the domain and range Identify whether it is a constant function f x x 11 Use the graphing tool to graph the linear equation Click to enlarge graph What is the domain Select the correct choice below and fill in the answer box to complete your choice OA The domain is a value or list of distinct values Type an integer or a simplified fraction Use a comma to separate answers as needed OB The domain in interval notation is Type your answer in interval notation What is the range Select the correct choice below and fill in the answer box to complete your choice O A The range in interval notation is Type your answer in interval notation OB The range is a value or list of distinct values Type an integer or a simplified fraction Use a comma to separate 15 9 B 45 12 6 Ay

Write an equation in slope intercept form for the line described x intercept 8 0 y intercept 0 1 The equation of the line is y Simplify your answer Type your answer in slope intercept form Use integers or fractic

15 cm 15cm C C 15 cm 123 15 cm p3 cm 9 cm 9 ca In the diagram the lengths of AB and AC are both 15 cm The point P is the foot of the perpendicular from C to AB The length CP 9 cm An are of a circle with centre B passes through C and meets AB at Q a Show that angle ABC 1 25 radians correct to 3 significant figures AP 15 9 2 AP IMY 1 2 cm 121

For the function defined as follows find a f x h b f x h f x and c N X 2 f x a f x h Simplify your answer f x h f x h

Find fog x and gof x for the pair of functions and give the doma f x g x 6 x 2 X Find fog x fog x

1 Let f x 6x 5 and g x Find f g x f g x fg x and 9 X domain of each f g x Simplify your answer x Give the

For the functions f x 6x 9 and g x 7x 9 find the following a fog x and its domain b gof x and its domain a fog x Simplify your answer

For a trip of x miles a taxi company charges f x 2 60 0 6 4x dollars a What is the cost of a 2 8 mile trip b What is the drop charge the fee applied as soon as the passenger enters the taxi c What is the distance charge for each quarter mile traveled a The cost of a 2 8 mile trip is Round to the nearest cent as needed

Match each equation with the sketch UI IS 3 2 2 Q f y x 5 ON 10 3 3 5 3 X 9 5 5 3 Q G OU 5 3 g y x 5 3 5 Drag each graph given above to the corresponding equation below a y x 5 b y x 5 7 5 k 3 o o o c y x 5 h y x 5 3

Match each equation in Column I with a description of its relates to the graph of y x a translation to the right 3 units a translation down 3 units a translation to the left 3 units a translation up 3 units Drag each description given above to the appropriate area below depending on the transformation of the function y x I a y x 3 b y x 3 c y 3x a vertical stretching by a factor of 3 d y x 3 e y x 3

he graph of y f x represents the amount Twater in thousands of gallons remaining m a swimming pool after x days y 52 48 44 40 Gallons in thousands 36 32 28 24 20 16 12 8 4 0 2 3 Time in days G X a Estimate the amounts of water contained in th pool The initial amount of water contained in the pool was thousands of gallons

Find the value of the function for the given value of x for x 5 f x The value of f x for x 5 is

Find the value of the function for the given value of x f x x for x 3 4 The value of f x x for x 3 4 is

cos 5x cos 4x cos3x Statement sin5 sin4x sin3x cos 5x cos 4x cos3x tan 4x Ru S

Determine the average rate of change in the winning time between 1964 and 2004 The following graph shows the fare rates for the Tortoise Taxi Co and the Crash up Cab Co 60 60 401 201 20 tot Question 3 1 point Taxi Fare Comparison Distance Driven km Tortoise Tax Crash up Cab noning of these values

The following graph shows the progression of world record times in the women S marathon Winning Time min 210 200 190 180 170 160 150 140 130 120 Women s Marathon Record Progression M 1964 1968 1977 1976 1980 1984 1993 1992 1996 2000 2004 2009 Year Question 1 1 point Describe any trends shown in the graph N

Find a general solution NOTE Write arbitrary constants as c and c Y1 y 4y 3y2 22 y2 6y15y2 4e t Y2

Scarlett buys a bag of cookies that contains 5 chocolate chip cookies 6 peanut butter cookies 7 sugar cookies and 9 oatmeal raisin cookies What is the probability that Scarlett randomly selects a sugar cookie from the bag eats it then randomly selects another sugar cookie Express your answer as a reduced fraction

Takoda has 12 marbles as shown in the diagram below Each marble is either blue or white In addition each marble is labeled with a number between 1 and 5 5 1 2 2 4 3 4 2 4 3 Takoda chooses one of the marbles at random Determine the following probabilities Enter your probabilites as fractions and simplify any fractions as needed What is the probability that Takoda will choose a blue marble given that the marble is odd What is the probability that Takoda will choose a odd marble given that the marble is blue

Suppose that f x x 6x 7 A What is the vertex of f B What are the x intercepts of the graph of f C Solve f x 7 for x What points are on the graph of f D Use the information obtained in parts A C to graph 2 f x x 6x 7

2 Find the following for the function f x 4x 2x 4 a f 0 e f x b f 4 f f x 2 a f 0 Simplify your answer b f 4 Simplify your answer c f 4 Simplify your answer d f x Simplify your answer e f x Simplify your answer f f x 2 Simplify your answer g f 3x Simplify your answer h f x h Simplify your answer c f 4 g f 3x d f x h f x h

x find the function g g x Simplify your answer Use integers or fractions for any numbers in the expression