Quadratic equations Questions and Answers

a x 5 30 26 Solve the quadratic equations by completing the square Round to the nearest hundredth if necessary a x 6x 40 b x 2x 1 0 27 Solve the quadratic equations by using the Quadratic Formula Round to the nearest hundredth if necessary a x 2x 15 0 b 2x x 8 0 c 5x 10x 5 28 Use the discriminant to determine the number of real solutions a x 4x 4 0 b x 14 14 Discriminant b 6x 2x 1 Discriminant c x 7x 1 Discriminant

15 Solve each equation after factoring fully a 3x 9x 54x 0 Vertex 3x x 3x 18 0 X 6 x 3 3x 0 AOS X 10 to 16 A X B 0 Domain x 0 a x 6 X Chapter 8 16 Identify characteristics of the quadratic function and its graph 3 37 Value A Ay AOS Range X 3 b 16x 360 X Circle one min or max Decreasing b Vertex Increasing Increasing 17 Find a the axis of symmetry and b the ankes at the graph of the function a f x 2x 4x 1 Vertex Domain c z 32 25z 75 0 13 Value Circle one min or max x 18 Tell whether the function has a minimum value or a maximum value Then find the value a f x 5x 10x 3 2x 16 AOS Range Decreasing

P 500 1 24 500 1 0175 F 500 X 45 4 7 You deposit 675 in a savings account that earns 6 interest compounded monthly write a function that represents the balance after t years 8 Solve the equation a 3 34x 9 Chapter 7 9 Write the polynomial in standard form Identify the degree and leading coefficient of the polynomial Then classify the polynomial by the number of terms a 6 2x Standard form Degree b 3p 5p6 4 Standard form Degree c 12y 8y Standard form Degree 10 Find the sum or difference a x 6x 5 2x 15 4 c 3a 7 a 1 Type Type Type b p 7 6p 13p LC LC LC y y 2 y 5y 2

28 f x x 5 x 2 y x int VA X HA Hole Domain

D If b varies jointly with a and c and b 112 when a 12 and c 7 find a when b 72 and c 2

Use the variation type to find the missing valu 39 w varies directly as r cubed and inversely as s If w 24 when r 4 and s 8 find r when w 81 and s 27

6p 13p 5 2p 17p 9 p 16p 63 4p 28

10 The following shows the average salaries based on age for two companies Age 20 29 30 39 40 49 50 59 Kodak Salary 32 000 40 000 52 000 70 000 Age 20 29 30 39 40 49 50 59 Panasonic Salary 35 000 41 000 48 000 60 000 Based on the data above which is true 1 Kodak s median salary is greater than Panasonic s median salary 2 Kodak s mean salary is less than Panasonic s mcan salary 3 The interquartile range for Kodak is less than the interquartile range for Panasonic 4 The first quartile at Kodak is greater than the first quartile at Panasonic

uppose that you deposit 5000 into a Certificate of Deposit CD today The deposit earns 7 interest compounded monthly a How long will it be before the account is worth 7000 D How long will it be before the account is worth 10000 That is how long will you have to wait until your money doubles

2 Solve the system of equations y 6x 11 2x 3y 7

4 A Volkswagen traveling at a constant rate of 55 miles per hour leaves Utica on the thruway One hour later a Subaru traveling at a constant rate of 65 miles per hour also leaves Utica traveling in the same direction on the thruway How long will it take for the Subaru to catch up to the Volkswagen if both vehicles continue in the same direction on the highway Volkswagon Subaru Rate mph Time hr Distance mi

Simplify 2 3 6 3 Do not use a calculator Write the exact simplified form

7 Write and solve an equation using the following Ten times the sum of twice a number and six is 40

Multiply and Simplify 5 2 7 5 Do not use a calculator

Multiply and Simplify 2 6 5 Do not use a calculator

Multiply and Simplify 4 5 7 Do not use a calculator

At a local Starbucks branch the weekly demand for croissants is given by q 800 200p where p is the price in dollars for a croissant and q is the number of croissants sold by the store in a week a 5 points What is the formula for the price elasticity of demand when croissants are priced at p dollars each b 4 points What is the price elasticity of demand at a price of 3 25 per croissant Interpret your answer in a sentence or two c 3 points How much should this Starbucks charge for a croissant to maximize weekly revenue Please give a one or two sentence summary on how you found this

Multiply and simplify 2 10 5 2 10 5

Simplify 6 Do not use a calculator Write the exact simplified fo

6 Given the line 2y 3x 10 which of the following points is not on the line Justify your answer 1 0 5 2 4 1 3 10 10 4 1 3

1 Letf be a function such that f x x 4 is defined on the domain 4 x 2 Write the range of the function using interval notation

Multiply and Simplify Do not use a calculator or round to a decimal Write the exact simplified form 5 7 3 21 35

f x 5x 2 8x and g x 2x 2 7 find f g x difference product quotient and composition of two functions

7 and 8 find the zero s of the function 7 y 6x 6 8 y x 9x 20 In Exercises 9 12 use zeros to graph the function 9 f x x 3x 10 11 f x x 9x 10 f x 2 x 3 x 1 12 f x 2x 12x 10x

Extra Practice In Exercises 1 and 2 find the x intercepts and axis of symmetry of the graph of the function 1 y x 2 x 4 2 y 3 x 2 x 3 In Exercises 3 6 graph the quadratic function Label the vertex axis of symmetry and x intercepts Describe the domain and range of the function 3 m x x 5 x 1 4 y 4 x 3 x 1 5 y x 4 6 f x x 2x 15

Consider the following function Prev Answe Answered Step 3 of 3 Identify the correct graph of this piecewise defined function 2 Points k x 5x 10 if x 2 if x 2 2 82 Enable Zoom Pan Enable Zoom Pan y

y 20 3x O is the origin 0 0 The points A and B lie on the line with equation y 20 3x Given that Cia mara find a noreib et of ardin int

Simplify 7m 5m 19 3m 19 10m 7m 24 21m 14m 35 4m 3m 14 10m 3m 19 1 ponto Solve for the variable Reduce the fraction to lowest terms If there is no solution say so 6 x 4 10 x 5 X 37 There is no real solution O x 3m 2m 5 x 17 2 37 x

Question 27 2 5 points In a connectel graph with no loops of multiple edges and with 28 edges waht is the maximum possible number of vertices 29 28 27 26 Question 28 2 5 points Which vertex listed below could be described as a TRANSMITTER OV

Consider the following relation y 4x 1 Step 1 of 2 Find four points contained in the inverse Express your values as an integer or simplified fraction Answer 2 Points C D D C D C

Consider the following relation Step 2 of 2 Find the domain and range of the inverse Express your answer in interval notation Answer 2 Points Domain Hange

In addition to a score 3 0 performance in depth inferences and applications that go beyond what was taught Heidi Teyah and Jared are having a contest to see who can launch a model rocket the highest Each rocket follows a quadratic trajectory Here are the equations for their rockets Heidi s rocket is f x 4 x 10 110 Teyah s rocket is f x 2x 24x 43 Jared s rocket is f x 3 x 2 x 14 Who won the contest Justify algebraically and show ALL of your thinking

EV Find a formula for the linear function depicted in the following graph 10 5 A A Enable Zoom Pan 5 10

Which of the graphs below correctly use Kurskal s Algorithm to determine a minimum spanning tree 5 D D Submit Quiz S 3 25 of 40 questions saved

Which graph below has an EULER CIRCUIT E L E

the following statement Vertex A and Bare ADJACENT

S The histogram below shows the heights of the students in Kyra s health class louerbes 160 169 170 179 180 189 190 199 200 209 Height cm a What is the total number of students in the class b How many people s height was less than 190 c How many people scored between 170 199

Question 11 2 5 points Sine Graphs What is the period of the sinusoidal equation 1 2T y 3 sin 2n x 1 4

Other Regression Models Using your calculator or graph paper create a scatter plot of the following data X 4 2 3 5 6 1 4 2 4 4 9 1 Which model would best represent data in the table Cubic 7 8 9 10 11 18 21 23 24 24 5 Sinusoidal Exponential Logistics Curve

0 00 9 12 15 18 Saved 21 Time Left 2 00 09 Neftali Moreno Miranda Attempt 1 Which data set below has the strongest correlation O O

11 7 1 11 3 12 17 15 0 21 18 24 Question 17 2 5 points Linear Regressions Which would be the best trend line for the given data set y x 4 y x 4 Oy x 2 O 10 10

A model rocket builder moved 50 feet away from the base before launching his model rocket straight up in to the air The rocket reached its maximum height when the angle of elevation from the observer was 84 Which equation below might help determine the maximum height of the rocket in feet sin 84 50 sin 84 50 tan 84 50 88 1 X 84 50 ft

What is the amplitude of the graph y sin 2x 6 3 01 2 3

9 12 15 Sine Graphs Determine the amplitude of the following Sine graph O K2 3 37 3m 2

a 12 15 Law of Cosines Determine the approximate value of d 5 cm R d A 4 29 cm 5 32 cm 6 24 cm 7 16 cm 8 cm 28 D

See Example 1 In Exercises 1 4 use the functions f x x 1 g x 2x 5 and h x 3x 3 to complete the table 1 19 1 201 3 0 1 2 1 1200 3 digsa in 4 nereriusin an 3 X 0 X g h x 1 01 h f x x 3x 7 g x x 7 x 11 g x x 3 WITH 6r 10 CalcChat AND CalcView Lidby 4 X 4 2 1024 X 4 10 20 Exercises 5 12 find a f g x b g f x and c f f x State the domain and range of each composit Example 2 f x 2x g x x 1 6 f x x 7 g x 2x 5 34 52 h g x f g x DALAGO Es 8 f x 4x 2 g x x 6 10 f x 6x 5 g x x

Suppose in an orchard the number of apples in a tree is normally distributed with a mean of 300 and a standard deviation of 30 apples Find the probability that a given tree has between 270 and 330 apples 270 300 330 360 390 P Hint Use the 68 95 99 7 rule 210 240 Enter

Over a weekend Jim counted the number of single scoop ice creams ordered at his store He tracked the flavors and the day on which it was ordered Chocolate Vanilla Cookie dough Saturday 1 5 6 Sunday 7 6 6 What is the probability that a randomly selected ice cream was cookie dough given that the ice cream was ordered on a Saturday Simplify any fractions

Joey works at a coffee shop on weekends Every now and then a customer will order a hot tea and ask Joey to surprise them with the flavor The teas are categorized by flavor and caffeine level Mint Fruity Chai Caffeine free Caffeinated 7 2 8 7 8 5 What is the probability that a randomly selected tea is fruity given that the tea is caffeinated Simplify any fractions

Consider the function f x x 4 x 1 x 5 x 36 Find the nonreal complex roots of f x