Quadratic equations Questions and Answers

2 If f x 3x 5x 7 find 2 O 15 O O O 7 05

1 Use the table below to find a prediction equation to show how altitude in thousands of feet relates to rainfall in inches Altitude Rainfall Oy x 3 y 3x 1 O y 2x 1 Oy x 3 0 2 5 12

Sketch a graph of x 1 8 7 Clear All Draw 465 I 6 5 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 3 2 1 2 2 3 4 5 6 7 00 3 4 5 8 Question Help Video 6

Simplify completely 435 5 2y4 11 Question Help Video

Select the correct answer The table gives the number of bacterial cells in a colony over time Time hours Cell Population 0 2 4 6 8 10 125 162 258 374 518 763 Fit an exponential model to the data Based on this model what is the best prediction for the number of cells in the colony at 16 hours A 2 300 B 1 200 C 1 600 D 2 700

If the supply and demand functions for a commodity are given by p q 10 and q 2p 10 1000 what is the equilibrium price and what is the correspond number of units supplied and demanded equilibrium price number of units MY NOTES Enter an exact number ASK YOUR TEACH

The supply and demand for a product are given by 2p q 50 and pq 100 20q respectively Find the market equilibrium point

2 3 2 1 2 0 2 6 8 10 Match each transformation of function fwith a feature of the transformed function function decreases as x increases vertical asymptote of x 2 h z g x 2f x f x 2 X j x f x 2 y intercept at 0 2 x intercept at 0 25 0

x 4x x 4 is a parabola with a hole in it x 4 What is the equation of the parabola What are the coordinates of the hole The graph of g x The equation of the parabola is y The coordinates of the hole are 1

If the supply function for a commodity is p q 5q 16 and the demand function is p 8q 8q 436 find the equilibrium quantity and equilibrium price equilibrium quantity equilibrium price

If a company has total costs C x 32 000 45x 0 1x2 and total revenues given by R x 525x 0 9x2 find the break even points Enter your answers as comma separated list X

Travis purchased a car for 25 000 He knows that the car loses 6 of its value every year Travis wants to determine what will be the value of his car after owning it for 6 years He completes the following steps A 6 A 6 25000 0 4 6 A 6 102 40 25000 1 0 6 6 Travis knows that his solution seems outrageous Describe where his error occurred fix the mistake and identify the appropriate value of the car Show your work using the Equation Editor Tool

a Graph the profit function P x 70x 0 2x 4000 y 4000 2000 200 100 2000 4000 y 4000 2000 200 100 100 X 200 300 400 500 100 200 X 500 400 300 4000 2000 200 100 2000 4000 4000 2000 y 200 100 y X 100 200 300 400 500 100 200 300 400 500 X MY NOTES P

Find the y intercept 2x 1 x 7 x 3 x 4 y 123 Enter the number that belongs in the green box

Condense the expression to a single logarithm x 36 log6y log6z log a

ane is saving her money in order to purchase a new racing bike She initially saves 3 and plans to double the amount she saves each month The ike Jane wants is 1 536 at the local bike shop Which equation represents this situation and after how many months t will Jane have enough money to purchase the bike A 3 2 1 536 t 11 B 32 1 536 t 9 C 3 1 2 1 536 t 35 D 3 2 1 536 t 9

a parallel to 2x 3y 4 Answer b perpendicular to x 2y 1 Answer Question 6 6 points The pressure P of water on a diver s body is a linear function of the diver s depth x At the water s surface the pressure is 1 atmosphere At a depth of 100 ft the pressure is about 3 92 atmospheres a Find a linear function that relates P to x b Compute the pressure to the nearest hundredth at a depth of 10 fathoms 60 ft Make sure to show the work leading to the answer

For the years since 2001 the percent p of high school seniors who have tried marijuana can be considered as a function of time t according to p f t 0 17t2 2 61t 52 64 where t is the number of years past 2000 Write a quadratic equation that can be used to find the year after 2000 that the percent is predicted to reach 60 if the function remains valid Solve the equation Eliminate any values that don t have meaning in the application Enter your answers as a comma separated list Round your answers to one decimal place t Use t to find the year after 2000 that the percent is predicted to reach 60

MY NOTES trees ASK YOU The yield in bushels from a grove of orange trees is given by Y x 1200x where x is the number of orange trees per acre How many trees will m yield

y 0 0001x 0 01 x y Find the zeros X Use the vertex and zeros to determine a range for a graphing utility that includes these values graph the function with that range 150 100 y 0 04 50 0 02 0 02 0 04 50 100 X 150 20 10 0 04 0 02 14 10 0 02 y 0 04 20 X

Find the exact real solutions to the equation if they exist Enter your answers as a comma separated list 4x 36 X

MYN If a ball is thrown upward at 64 feet per second from the top of a building that is 140 feet high the height of the ball is given E S 140 64t 16t feet where t is the number of seconds after the ball is thrown How long after it is thrown is the height 140 feet t S

7x 21 Place the steps for finding f z in the correct order x 21 7y x 7y 7y 21 x 3 y y 7x 21 x 21 7y 3 f x where x 0 x 7y 21 x 21 f x where

Solve the equation 5x 2 3x 5 4x 11 x X Enter

Use Desmos or a Graphing Calculator to solve the equation 42 2 x 12

Martha took out an 8 year loan of 35 790 to purchase a sports utility vehicle at an interest rate of 6 2 compounded monthly How much will she have to pay in 8 years Two decimal answer

Brianna was given 2000 at birth Her parents invested the money at a 2 interest rate compounded quarterly No deposits or withdrawals were made Which equation can be used to determine how much money Brianna will have in the account when she turns 13 O A 2000 1 0 02 4 13 13 O A 2000 1 0 02 O A 2000 1 O 2000 1 0 02 4 A 2000 1 0 02 4 13

Let f x 3x 4 and g x x 2 Find f g x and its domain

Solve the system of equations x y 5 x 5y 9 x O 1 2 O 4 1 O 10 15 O 5 10

The system of equations of y 2x 2y 4x What could it be classined as Consistent Independent System Consistent Dependent System Inconsistent System represents what kind of system

For x 0 which answer best describes the curve of the function f x 2 x

Use the dropdown menus to match the letter of the equations with the graph that can be used to solve it a 2 3 3 50 3 5 4 2 3 8 4 6 4 A 4 A 2 4 4 4 10 4 2 2 4 4 9 2 99 2 4 b 3 1 3 2 2 2 4 2 4 6 4 6 1 10 c 4 3 Select Select Select Select

Enter the equation g x 2 3 2 1 and f x 3 How does the graph g x differ from the graph of f x Select all that apply The graph compressed horizontally by a scale factor of 2 The graph translates up 1 unit The graph translates left 2 units The graph compressed vertically by a scale factor of 2 The graph reflected across the x axis The graph reflected across the y axis

Identify the key features of the function from the table X 2 1 0 1 2 a 1 b 1 0 b 1 a 4 f x 16 14 b 4 1 4 O The y intercept is 0 1 The function is increasing 16 O The x intercept is 0 1 The function is decreasing

5 Use Desmos or a Graphing Calculator to solve the equation 2 1 X

Oliver would like to buy some new furniture for his home He decides to buy the furniture on credit with 9 5 interest compounded quarterly If he spent 5 400 how much total will he have paid after 7 years Two decimal answer

Eugene s parents put 2 500 in a bank account for college tuition at an interest rate of 8 75 compounded semiannually What will be the balance after 18 years Two decimal answer

initial investment Question 4 mly After 3 years the balance reaches 1 O Wildt was the amount of the 1 pts

The Anderson s took out a loan for 195 000 to purchase a home At 4 3 interest rate compounded annually how much will they have paid after 30 years Two decimal answer

Jana invests a sum of money in a retirement account with a fixed annual interest rate of 2 15 compounded continuously After 10 years the balance reaches 1 912 41 What was the amount of the initial investment

Enter the equation g x 2 4 and f x 2 How does the graph g x differ fron the graph of f x Select all that apply The graph translates down 4 units The graph compressed horizontally by a scale factor of 3 The graph reflected across the x axis O The graph translates right 3 units The graph compressed vertically by a scale factor of

Annual sales for a company were collected over a period of time Data was collected on the amount of sales per 1 000 dollars The graph shown displays some of the data that was collected for the first 10 years Based on the graph during which year were there approximately 247 000 dollars in sales 13001 285 270 255 Annual Sales per 1 000 dollars 240 225 210 195 180 165 150 135 120 105 90 75 60 45 30 15 2 1 0 15 Week 4 Week 6 1 Week 8 2 3 4 5 6 7 f T This image cannot be easily described If you need an explanation of this image please ask your teacher for help A 8 9 10 11 12 13 14 years

The growth rate of mosquitoes per month from the beginning of summer is displayed below Identify the initial amount of mosquitoes the growth rate the growth factor and the number of mosquitoes there will be after 5 months Select all that apply n 0 1 2 n 3 t n 3000 4500 6750 O The growth rate is 50 10125 O The growth factor is 1 50 O The initial amount is 3000 TI O The number of mosquitoes after 5 months is 22 781 O The growth factor is 0 50 The initial amount is 4500 The growth rate is 150 i 21171

A golf tournament begins with 128 players At the end of round one there will be 64 players There are 32 players at the end of round 2 and 16 players remaining at the end of round 3 Which equation best models this situation O y 128 0 5 O y 0 5x 128 O y 128 2 O y 64x 128

A colony of 800 ants is decaying by 13 daily Which equation below could be used to find the number of ants for any specific day Let N represent the number of ants left in the colony and let d represent the number of days ON 800 0 13 ON 800d 0 87 N 800 13d ON 800 0 87

Enter the equation f x g x differ from the graph of f x and g x O The graph translates down 7 units O The graph translates to the right 7 units The graph translates to the left 7 units O The graph translates up 7 units 1 7 in the Desmos Graphing Calculator 3

Finance Plan Product Stove 2000 00 20 Down Payment 400 00 Price Discount A 1 580 00 B 1 200 00 C 1 898 00 D 1 520 00 What is the amount owed for an installment loan to purchase the item described in the table

In the diagram below PQRS is a parallelogram with diagonals PR and QS QY and XS are drawn such that QY XS L 2 3 P 2 1 Y 2 1 M 2 Q Use the diagram to prove each of the following 6 1 AQPY ASRX 6 2 QYSX is a parallelogram 6 3 YM MX X 1 12 2 1 R 1 2 3 S

The arc lenght of the curve t 2t i j In t k for 1 tse is A 5 2 B 97 D 11 1

Solve the initial value problem x t Ax t for t20 with x 0 5 2 Classify the nature of the origin as an attractor repeller or saddle point of the dynamical system described by x Ax Find the directions of greatest attraction and or repulsion A 16 1 4 11