Quadratic equations Questions and Answers

Use polynomial long division to evaluate 21x 56x 28 3x 5 and write 21x 56x 28 in the form 21x2 56x 28 21x2 56x 28 divisor quotient remainder

Which functions are odd or even a f x sec x is b f x csc x 2 is c f x sec x csc x is d f x 5csc x is e f x 1 sec x is f f x sec 4x is

Which of the following functions has the same horizontal asymptote as the function graphed below 5 5 0 5 f x 4 2 3 f x 4x 3 2 Of x 4 3 2 f x 3x 2 1

3 A L B a Note Triangle may not be drawn to scale Given the triangle above find the following Give exact values No decimals allowed sin A cos A tan A sec A csc A cot A

The graph shows stopping distances for trucks at various speeds on wet roads Use this information to complete parts a and b below f x x x opping Distance feet Stopping Distances at Selected Speeds 700 620 600 500 445 400 305 300 185 200 85 100 0 25 35 45 59 55 a Use the statistical menu of your graphing utility and the quadratic regression program to obtain the quadratic function that models a truck s stopping distance f x in feet on wet pavement traveling at x miles per hour

1 6 pts Rewrite the rational function g x are constants x 7 X in the form g x c where c and r

Solve 7sin Pi 6x 3 for the four smallest positive solutions

88 3a 4b

1 Point What is the maximum number of real zeros for the following polynomial p x 2x5 4x 10

Given that f x x 6 and g x 7 5x find a f g 2 b g 2 c fg 2 d 2

Solve the following system y i y Give the answers in the form of a fraction if necessary 18 2

An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 feet from each corner and turning up the edges See the figure on the right If the box is to hold 864 cubic feet what should be the dimensions of the sheet metal

9 The point of view used by the author gives the reader insight into the O family s behaviors Pashtun tribe O narrator s thoughts brothers feelings

Given that f x 2x 5x 1 and g x zh a Determine the rule for the composite function g g x g g z b Determine the rule for the composite function g f z g f z c Determine the rule for the composite function f g f g x Preview Preview Preview

Please show all work for full credit Round to two decimal places when necessary 1 Write the interval notation for the solution graphed below 1 10 9 1 1 1 6 1 3 1 2 1 1 1 2 1 3 5 1 6 7 a

You may need to use the appropriate technology to answer this question Consider the experimental results for the following randomized block design Make the calculations necessary to set up the analysis of variance table Blocks 1 2 3 4 Treatments A B C 10 9 8 12 6 5 18 15 14 OHO HA HB HC Ha HA HB c 20 19 18 5 8 7 St for any sign ant differences Use 0 05 to State the null and alternative hypotheses OHO HA HB c Ha HAHB HC HO HA HB MC H Not all the population means are equal O Ho At least two of the population means are equal H At least two of the population means are different

Part 3 of 3 What age corresponds to the standard value of 3 2 010 6

A survey is taken of people entering a stadium The selected individuals are 20 70 120 170 220 Systematic Stratified Cluster Simple Random

Part 3 of 3 The percent of showers that use between 10 9 and 20 1 gal 9 10 3 X

10 11 5 Find Q1 12 17 15 7 2 11 15 1 12 9 Part 2 of 3 Find Range Part 3 of 3 16 58 2 16 X 8 16 X 5 6

A doctor measured serum HDL levels in her patients and found that they were normally distributed with a mean of 69 4 and a standard deviation of 3 9 Find the 2 decimal serum HDL levels that correspond to z 1 6 Part 2 of 2 00 X 19 A doctor measured serum HDL levels in her patients and found that they were normally distributed with a mean of 69 4 and a standard deviation of 3 9 Find the 2 decimal serum HDL levels that correspond to z 2 74 E In P C

In a mid size company the distribution of the number of phone calls answered each day by each receptionist is bell shaped and has a mean of 42 and a standard deviation of 12 Using the empirical rule what is the approximate percentage of daily phone calls between 18 and 42 do not put the percent symbol Part 2 of 3 00 X 1 9 What is the percent between 30 and 54 do not put the percent symbol

Use the table of values to find each 2 d cimal answer 21 74 84 60 23 45 88 29 36 27 60 37 58 41 77 57 31 27 63 76 88 64 92 16 Find the mean Part 2 of 3 010 S If this is sample data give the sample standard deviation

For what value of k will the linear system below be consistent Try to do this problem with pencil and paper only 121 322 721 421 512 k 12 k 6 6

Find all real solutions of the equation by factoring Enter your answers as a comma separated list 4x 4x3 0 X

7w 3 2w 4 11

22 5 6v 1 63

The function g is related to one of the parent functions described in an earlier section g x x 6 a Identify the parent function f f x b Describe the sequence of transformations from f to g Select all that apply O reflection in the x axis horizontal shift of 6 units left Overtical shift of 6 units upward Overtical shrink Ohorizontal shift of 6 units right c Sketch the graph of g O y y 5 10 5 4 2 2 4 V V 5 15 10 5 10 5 4 2 15 y 15 10 5 5 2 d Use function notation to write g in terms of f g x f 4 X X 15 10 10 M y 10 5 5 10

Solve the following system of equations graphically on the set of axes below 1 2 5 y 10 9 8 7 6 5 y x 4 Plot two lines by clicking the graph Click a line to delete it 3 2 1 7 1 N 2 co 759 2 10 7 5 1 2 9 10 x

additional parentheses 000000 1 5x 3 2 2 5x3 4 25 2 15 2 2x2x2 3 3 x 5 13 441 25420H 3 4 3 x 4 3 25 4 3 X 6 2x2 5 4 5 10 2 2 1 5 6 1 3 2 6 x 2 5 2 8 X7 56 8 3 2 2 17 7 5 1 5 5

6 2 2 8 4 V 10 2 2 1 6 V6 13 26X2 5 28 VR 36 8 3 2X2 17 V8 7x4 3X6 5 1 50

Use Gauss Jordan row reduction to solve the given system of equations system is dependent express your answer using the parameters x y ar x y z 8x y 32 0 8x y 2z 5

Match the graph with its function using the x intercepts 4 4 4 4 24 y x x 2 y x x 2 y x x 2 y x x 2

A ball is projected upward from the ground Its distance in feet from the ground in t seconds is given by s t 16t 126t At what times will the ball be 223 feet from the ground

A conical tank contains seawater to a height of 2 ft The tank measures 12 ft high and 5 ft in radius Find the work needed to pump all the water to a level 2 ft above the rim of the tank lb The specific weight of seawater is 64 ft3 Approximate the answer to three decimal figures

One leg of a right triangle is 2 millimeters longer than the shorter leg and the hypotenuse is 4 millimeters longer than the shorter leg Find the lengths of the sides of the triangle The length of the shorter leg is The length of the longer leg is The length of the hypotenuse is millimeters cubic millimeters square millimeters

The length of a rectangle is 19 centimeters less than five times its width Its area is 30 square centimeters Find the dimensions of the rectangle The width is and the length is

The product of two consecutive room numbers is 306 Find the room numbers The number of the first room or the smaller room number is x 1

Part 4 Write a real world situation for each expression below be creative A b 12

The function h defined by h t 49 4 9t 10 t models the height in meters of an object seconds after it is dropped from a helicopter b C Find or approximate the time when the object hits the ground Explain or show your reasoning From what height is the object dropped Explain or show your reasoning Where is the vertex of the graph

3 A quadratic function is defined by g x x 4 7 What is the vertex of the graph of function g C a b Does the vertex represent the minimum value or the maximum value of the function Explain or show how you know If you were to shift this graph 6 units down from where it is now what would be the equation represented by the new graph

NAME T Introduction to Quadratic Functions Assessment 2 Here is the graph of a quadratic function f 1 2 a b C y 1 O 1 2 3 4 5 6 2 0 2 6 0 3 4 5 5 DATE 2 2 24 4 4 7 X Write the equation for f x in vertex form Write the equation for f x in factored form Write the equation for f x in standard form 2 A quadratic function is defined by p x x 1 x 3 Graph the function on the coordinate plane and label the coordinates of the x intercepts the y intercept and the vertex y 5 4 3 2 1 WN TO 6 5 4 3 2 10 1 2 3 T 2 3 4 PERIOD 5 X

troduction to Quadratic Functions Assessment 2 Here is the graph of a quadratic function f y 1 2 1 a b C 1 2 3 4 5 2 0 2 3 4 6 0 5 en 4 4 16 7 X Write the equation for f x in vertex form Write the equation for f x in factored form Write the equation for f x in standard form

2 2 3 Select Select Two numbers multiply together to equal 90 but add together to equal 9 What are the two numbers Select 4 Select 5 6 and 1 7

2 2 Two numbers multiply together to equal 90 but Select add together 9 What are the two numbers Select t Select 2 Select and 1

6 2x 2 10 When you square both sides what is the resulting O equation in the next step before you solve for x O O 2x 2 100 2x 2 10 1 2x 2 100 2x 2 10 C

b Where are the x intercepts d Where is the y intercept e Where is the vertex f Graph the function on the coordinate plane and label the coordinates of the x intercepts the y intercept and the vertex X

Convert the degree measure to exact radian masuro 170 dog

What is the quotient of 3x4 4x2 8x 1 x 2 Watch for any missing terms 3x 6x 8x 24 47 x 2 3x 6x2 8x 24 47 3x 6x 8x 24 3x 4x 8x 1 47 3x 4x 8x 1 O3x 6x 8x 24 47 X 2

Joshua decides to use synthetic division to find the quotient of 3x 8x 2x 3x 10 x 2 What value from the divisor should he write in front of the coefficients 00 3 S S