Quadratic equations Questions and Answers

Simplify the following rational function assuming the denominator is is nonzero x 2x 8 x 4x 12 Give your answer as a simplified rational expression Do not include f x or the domain restrictions in your answe Drouide YQUE DE f x

Two babysitters charge the following Fred charges 4 per hour George charges 1 per hour in addition to a base charge of 6 Use graphing to find the point where the two will charge the same amount O 3 hours 10 1 hours 5 O 8 hours 2 O2 hours 8 None of these choices are correct

1 c 5 6pts For each table below could it represent a function that is linear exponential or neither a b X h x X X 1 f x 70 X g x 1 2 3 4 40 10 20 1 2 3 4 40 32 26 22 1 2 3 4 80 61 42 9 25 61 2 3 4

14 8pts Find an equation for the exponential graphed Hint locate the horizontal asymp first a b 2 23

Solve for b Do not include b in your answer a 96 4 b 9

Use the marginal analysis criterion covered in class to find the number of units x that produces the minimum average total cost per unit C in the given equation C x 0 001x 9x 54 X units X

a relationship between two quantities from a graph a written description or a table of values within a mathematical or real world context 10 5 T 10 5 0 5 8 LO 5 10 an exponenti function that represents the graph below f x

Suppose that i 57 4j and v 6i 7j are given Compute the given linear combination of these two vectors 3u v 1 09 1 the

ction is given 50 1 1 Part A Does this function represent exponential growth or decay Part B What is the constant percent rate of change of y with respect to t Exponential Growth Exponential Decay

exponential function is given by the 14 1 x asymptote for the graph equation 14 What is the

station 4 Find the value of x 32 102 d 124 160

A rectangle is drawn so the width is 6 inches longer than the height If the rectangle s diagonal measurement is 60 inches find the height Give your answer rounded to 1 decimal place inches

Solve by the quadratic formula List the solutions separated by commas 25x 5x 6 T

orld problems that are modeled with uadratic functions Interpret key features nd determine constraints in terms of the Ontext T X S 1972 can be modeled by the function 19 252 440 3500 where t is the number of years since 1972 Part A In what year does the car s value start to increase 22222 Submit Part B Will the car s will ever begin to olad

The equation of a parabola is y x 10x 16 Write the equation in vertex form Write any numbers as integers or simplified proper or improper fractions

Determine the solutions of the equation below 3 2 14 14 X

Given the function 125 1 0 26 does it represent an exponential growth or decay function Exponential Growth Exponential Decay

Suppose that the functions f and g are defined as follows f x 2x 2 5 g x 8x 6 Find all values that are NOT in the domain of f g find f g 2

Given an expression or equation epresenting a quadratic function determine the vertex and zeros and interpret them in terms of a real world context T X S Marcus just purchased a Super Bouncy Ball from a local toy store Once outside he throws it down to see how high the ball will bounce The function h 2 24 31 5 represents the height h in inches above the top of his head of the ball as it relates to its horizontal distance from Marcus x in inches Find the zeros and vertex of this function Discuss their meaning in terms of this context X Submit

Write a quadratic function to represent the relationship between two quantities from a graph a written description or a table of values within a mathematical or real world context 10 T 10 5 0 5 10 5 10 Write the quadratic function that corresponds with the graph below f x Sub

The equation y 2 x 1 2 5 is graphed in the xy plane Which of the following statements about the graph is true

Graph the solution to the inequality on the number line x 5

A toy racecar races along a circular race track that has a radius of 31 meters The racecar starts at the 3 o clock position of the track and travels in the CCW direction a Suppose the racecar has traveled 52 meters along the race track i How many radians has the racecar swept out radians Preview ii What is the racecar s distance to the right of the center of the race track in meters meters Preview iii What is the racecar s distance above the center of the race track in meters meters Preview b Let d represent the racecar s varying distance traveled in meters along the circular race track i Write an expression in terms of d to represent the racecar s distance to the right of the center of the race track in meters Preview ii Write an expression in terms of d to represent the racecar s distance above the center of the race track in meters Preview

Given the table of values below from a quadratic function write an equation of that function X f x f x 6 2 5 1 4 2 3 1 2 2

2 A new coffee shop wants to maximize their profit within the first year of business They determined the function P x 80x 480x 540 models the profit they can earn in thousands of dollars in terms of the price per cup of coffee in dollars What price of coffee maximizes the coffee shop s profit Brico

What are the exact solutions to the equation s x X 0

Write two variable linear inequalities to represent relationships between quantities from a graph or a written description within a mathematical or real world context 10 T 5 10 5 0 5 X 10 The graph of the solution set to a linear inequality is shown below Create a linear inequality that corresponds to this graph Subr

What are the solutions to the equation 2 0 25x 4x 0 75 Round to the nearest tenth if necessary

and v Compute the area of the parallelogram determined by u v u v and 0 and compute the determinant of u v ce the first entry of v by an arbitrary number x and repeat the problem Draw a picture and explain what you find How do they comp

The expression 45 225 represents the total cost in dollars of renting a large party tent from a local rental store for hours Jamal s parents are willing to spend between 500 and 750 for the tent Part A Write an inequality to represent the possible lengths of time the tent can be rented Part B Using your inequality in Part A what is one possible length of time the tent could be rented Give your answer in number of hours 5 hours 8 hours 12 hours 15 hours Submit

Solve and graph mathematical and real world problems that are modeled with linear functions Interpret key features and determine constraints in terms of the context 8 28 75 27 5 26 25 T Suppose you fill your truck s tank with fuel and begin driving down the highway for a road trip Assume that as you drive the number of minutes since you filled the tank and the number of gallons remaining in the tank are related by a linear function After 40 minutes you have 28 5 gallons left An hour after filling up you have 26 25 gallons left Part A Graph this relationship Part B Determine how many hours it will take for you to run out of fuel Round to the nearest hundredth of the hour Submit

8 Name three factors you would consider crucial for the development of life on another planet Why are they important

2 Which elements were formed during the Big Bang and how was it possible for Nucleosynthesis to occur then

3 Ch 13 Describe one method for detecting extrasolar planets Give the name of the method and explain how it works Use online resources to report on one planet discovered using this method

1 Ch 12 How is the Hubble Constant H related to the age of the universe Hypothetically if the value of the Hubble Constant were 700 km s Mpc what would this imply about the age of our universe Hint is this hypothetical value of H larger or smaller than the actual value

Part A Graph the function g x 3 6x 7 Part B Identify the domain range and x and y intercepts of the function Please express domain and range in inequality notation Round to the nearest tenth when needed Domain Range y intercept K SEF Submit Submit

The formula d 0 2 trelating to the translational of motion where d represents distance vo represents initial velocity v represents final velocity and t represents time Rearrange the formula to isolate final velocity

Given a table equation or written description of a linear function graph that function and determine and interpret its key features 10 T 5 2 5 1 25 0 1 25 S 5 X 10 Graph the linear function represented in the table belo X f x 3 2 5 1 1 5 7 0 9 0 5 18 2 75

Write an equation for the line that passes through 3 14 and is parallel to the line that passes through 10 2 and 25 15

A group of friends decides to go out of town to a championship football game The group pays 185 per ticket plus a one time convenience fee of 15 They also each pay 27 to ride a tour bus to the game If the group spent 2 771 in total how many friends are in the group

Write a linear function for a line that passes through the point 4 3 and is perpendicular to y 0 25x 9

What is the quotient of the expression 3 2 2 2 58 12 12 3 12 x y xy X

2 Given the polynomial x product of polynomials 10x 24 rewrite it as a

Determine the sum of the expression 1 2 x 2 3 3 x 4 2 3 x x 5 6

2 Given the polynomial x3 3x 9x 27 rewrite it as a product of polynomials

Determine the value of the expression 4 10 3 15 Write your answer as an exact quantity using only a single radical

Determine the difference of the expression 2 0 4x 0 5x 2 0 6 x 0 5x

The surface area s r in square meters of a spherical balloon with radius meters is given by S r 4xr The radius P 1 in meters after seconds is given by P t 1 Write a formula for the surface area N 1 in square meters of the balloon after seconds It is not necessary to simplify

10 4pts Match each function with one of the graphs x A x B f x x A x B g x B h x x A x B C k x x A x B D

Which equation matches this graph 3 O 2 1 O y 3x 6x 1 2 None of these choices are correct y x 2 3 Of x x 3 Oy x 2 3