Quadratic equations Questions and Answers

3 Maya s gas tank currently holds 9 gallons of gas It is 60 full How much gas can the tank hold when full

1 point Suppose and Then f g x x 2 x 2 f g x x 2 x fg x x 3 x 2 x 1 f g x x 2 1 x 1 f g x x 2 2x 2 g f x x 2 2 and f x x 1 g x x 1

LINE y 3x 1 5 Determine the y intercept of a line with a slope of 2 that is a tangent to the curve y 2x 6 4x

4 On a test there are 6 true false questions 5 multiple choice and 4 short responses What percent of the questions on the test are true false

A catering company prepares and sells food items Let x be the number of items prepared and sold in one month The cost function is C x 1200 120 x The revenue function is R x 150x Find the profit or loss when 200 flat screen TVs are sold When the company prepares and sells 200 items in one month the profit is 6000 When the company prepares and sells 200 items in one month the profit is 7200 When the company prepares and sells 200 items in one month the profit is 4800 When the company prepares and sells 200 items in one month the loss is 4800

store sells small notebooks for 8 and large notebooks for 16 If a student buys 6 notebooks and spends 80 how many of each size did he buy He bought small notebooks and large notebooks Type whole numbers

4 80 of a class completed the homework one night If there are 20 students in the class how many students completed the homework A 8 B 16 C 18 D 25

The price of a home is 250 000 The bank requires a 15 down payment and two points at the time of closing The home is financed with a 20 year mortgage at 6 5 compounded monthly Find the amount of the monthly payment Payment 11 1 1 1584 34 1863 93 2798 18 1552 66

se a coterminal angle to find the exact value of the following expression Do not use a calculator 9x 4 sin

Linda needs to have her car towed Little Town Auto charges a flat fee of 85 plus 2 per mile towed Write a function expressing Linda s towing cost c in terms of miles towed x Find the cost of having a car towed 11 miles c x 2x 22 c x 2x 85 Oc x 2 85 c x 2x 85 97 87 107

Use the graph of y f x to answer the following y f x Part 0 9 Part 1 of 9 a Determine f 0 f 0 3 2 1 4

The price of a home is 260 000 The bank requires a 20 down payment After the down payment the cost of the home is financed with a 15 year fixed rate mortgage at 7 Find the mortgage loan amount 241 800 52 000 208 000 O 260 000

Select all functions that will successfully return value s based on the parameter list inputs back to the invoking program such that the values can be used for later computation after the function has ended Odef mystery1 x y a b y x return a b Odef mystery2 w1 w2 x y w2 w1 print x y def mystery3 X V V X

Find how much money will be in the account after the given number of years at the given rate of compound interest Principal 7000 Rate 4 compounded semiannually Time 4 years Use one of the formulas below to solve the problem Future Value A P 1 nxt Present Value P 7577 03 9579 98 8201 62 8189 01 nxt

The price of a home is 180 000 The bank requires a 5 down payment at the time of closing The cost of the home is financed with a 30 year fixed rate mortgage at 7 5 Find the required down payment 13 500 O 135 000 O 90 000 O 9 000

A dress regularly sells for 67 The sale price is 52 Find the percent decrease of the sale price from the regular price 22 4 346 7 28 8 O 77 6

Listen Suppose that the luxury sales tax rate in a foreign country is 19 A very wealthy socialite bought a diamond tiara for 168 000 How much tax does she pay 31 920 3192 319 n

Exit Ticket 10 16 1 At a school 40 of the students play a sport If there are 80 athletes at the school how many students are there in the school A 32 B 200 C 320 D 3200

100 90 80 70 60 50 40 30 20 10 Grade 9 ELA Midterm Grade Report Blology Algebra 1 U S History Art What is the difference between Gabrielle s greatest score and least score

One factor of f x x 12x 47x 60 is x 5 What are the zeros of the function 05 4 3 O5 4 3 O 5 4 3 O 5 4 3

Given f x x 1 x 2 x 3 what are the zeros and end behavior of the function O1 2 3 continues downward to the left and upward to the right O 1 2 3 continues downward to the left and upward to the right O 1 2 3 continues upward to the left and downward to the right O1 2 3 continues upward to the left and downward to the right

What are the zeros of the function f x x 4x 5 5 ti O 2 i O 5 ti O 52 1

The graph of f x is shown 5 O 4 0 2 O 2 0 4 For what values of x does f x 0 O 5 0 17 15 0 17 0 5 10 0

Without using technology describe the end behavior of f x 3x4 8x 22x 43 O Down on the left down on the right Down on the left up on the right O Up on the left down on the right O up on the left up on the right

The volume of a rectangular prism is represented by the function x 11x 20x 32 The width of the box is x 1 while the height is x 8 Find the expression representing the length of the box Ox 6 Ox 4 Ox 4 OFFE

Determine whether the function f x 4x is even or odd O The function is even because f x f x O The function is odd because f x f x O The function is even because f x f x O The function is odd because f x f x

Let f x 8x 28x 61 and g x 2x 5 Find O4x2 10x 34 O4x 10x 34 O4x210x 11 O4x 10x 11 116 2x 5 2x 5 116 2x 5 6 6 2x 5 f x g x

Use synthetic division to evaluate 3x 6x 3 x 1 3x 9 O3x 3x 3x 3 3x 6

Divide 2x 17x 35 by x 5 Ox 7 O 2x 7 Ox 27 O 2x 27 G

Which answer best describes the complex zeros of the polynomial function f x x x 10x 10 The function has one real zero and two nonreal zeros The graph of the function intersects the x axis at exactly two locations The function has one real zero and two nonreal zeros The graph of the function intersects the x axis at exactly one location The function has two real zeros and one nonreal zero The graph of the function intersects the x axis at exactly one location O The function has three real zeros The graph of the function intersects the x axis at exactly three locations

Name 1 Data collected during an experiment are shown in the accompanying graph Percent Maximum Activity of Trypsin 100 75 50 25 y 0 X 1 2 3 4 5 6 7 8 9 10 pH What is the range of this set of data A 2 5 y 9 5 C 0 y 100 B 2 5 x 9 5 D 1 x 10 2 The acc certain D along a Elevation ft 1600 1500 1400 1300 1200 1100 1000 900 What is A 1 0 C 0

Factor f x into linear factors given that k is a zero of f x f x 4x 13x 50x 75 k 5 f x Factor completely

Triangle ABC has sides measuring AB 7m BC 5m and AC 9m What is the width of the largest rectangle that can be inscribed in it with the longer side of the rectangle along the 9 m side a 2 521 m b 1 934 m c 3 156 m d 3 712 m

3 15 20 Position velocity and acceleration Suppose the position of an object moving horizontally along a line after t seconds is given by the following functions s f t where s is measured in feet with s 0 corresponding to positions right of the origin 1 a Graph the position function b Find and graph the velocity function When is the object stationary moving to the right and moving to the left c Determine the velocity and acceleration of the object at t 1 d Determine the acceleration of the object when its velocity is zero e On what intervals is the speed increasing 15 f t 12 4t 0 t 5 16 f 1 1 4t 3 0 t 5 17 f t 212 9t 12 0 t 3 18 f t 18t 31 0 t 8 19 f t 21 211 601 0 t 6 20 f t 61 3612 54t 0 t 4 21 A dropped stone on Earth The height in feet of a stone dropped from a bridge 64 feet above a river at t 0 seconds is given by s 1 1612 64 Find the velocity of the stone and its speed when it hits the water H I 22 A dropped stone on Mars A stone is dropped off the edge of a 54 ft cliff on Mars where the acceleration due to gravity is about 12 ft s The height in feet of the stone above the ground I seconds after it is dropped is s 1 ity of the stone and its speed when it hits the ground 61 54 Find the veloc 23 Throwing a stone Suppose a stone is thrown vertically upward from the edge of a cliff on Forth

Practice 1 Given the equation n 81 321 solve for n n 81 321 n 1 Given equation Add from both sides Simplify 2 Sol LE

Air temperature decreases as altitude increases If the ground temperature is 72 F then the air temperature x miles high is T 72 19x a Determine the altitudes x where the temperature T is between 2 F and 32 F b Use an absolute value inequality to describe these altitudes a Determine the altitudes x where the air temperature T is between 2 F and 32 F inclusive 19 x 19 Type an integer or a simplified fraction

The hypotenuse of a right triangle is 6 5 cm longer than one leg and 12 2 cm longer than the other leg Let x represent the length of the hypotenuse Pak2Q1 1 Draw and label all information given in a right triangle form format below 2 Use the Pythagorean Theorem to create a quadratic equation in standard form format that can be solved for x then using the information given and DESMOS solve below 3 From DESMOS just use one of your x solutions Xints roots zeros just one to prove that your x from DESMOS is the solution round Xints to the tenth position close is okay 4 Using DESMOS as your guide draw out your QE Label your Xaxis Yaxis scale to scale Label the Xints and the Yint on the Cartesian Plane provided above

Suppose that a ball is thrown from the top of a 88 foot building The function h t 16t 72t 88 models the height in feet h of the ball t seconds after it is thrown a Find the zero s of the function You may use fractions or decimals Use a comma to separate values if necessary The zero s of the function b If we assume that ground level means h The ball hits the ground after c Find the time s the ball will be 144 feet above ground You may use fractions or decimals Use a comma to separate values if necessary The ball is 144 feet above ground after d The ball will be at its highest point after t 2 25 seconds Find the height of the ball at that time The height of the ball after 2 25 seconds is 0 when does the ball hit the ground Select an answer Select an answer Select an answer

Consider the function f x 4x 49 a Determine the zeros of the function Writing values as simplified fractions if necessary If there are multiple values separate the solutions with a comma If there are no values input DNE b Determine the x intercept s of the graph of the function Write ordered pairs writing any values as simplified fractions if necessary If there are multiple x intercepts separate them with a comma If there are no x intercepts input DNE c Determine the y intercept s of the graph of the function Write ordered pairs writing any values as simplified fractions if necessary If there are multiple y intercepts separate them with a comma If there are no y intercepts input DNE

Solve the equation writing solutions as simplified fractions if necessary If there are multiple solutions separate the solutions with a comma If there are no solutions input DNE 7y 4 0 Solution y

p Find s given that 1 3 lies on the line with equation y sx

6 LO 4 3 2 1 10 1 2 3 4 5 6 7 8 2014 9 10 11 12 13 14 15 16

Notice that the curve given by the parametric equations x 81 t y t 1t is symetric about the x axis If t gives us the point x y then t will give x y At which x value is the tangent to this curve horizontal At x At which t value is the tangent to this curve vertical Att The curve makes a loop which lies along the x axis What is the total area inside the loop Area Graph the curve on a calculator Turn in a sketch of the curve

The polynomial function f has exactly one positive zero Approximate the zero correct to two decimal places 3 f x 2x 16x 5x 8x 3 The positive zero of f is approximately Round to two decimal places as needed

3 Find k such that f x x kx kx 8 has the factor x 4 Simplify

Use the rational zeros theorem to list the potential rational zeros of the polynomial function Do not attempt to find the zeros 7 5 4 f x 2x x 2x 20 Find the potential rational zeros Choose the correct answer below OA 1 1 2 2 4 4 5 5 20 20 1 1 2 2 OB 1 1 2 2 4 4 5 5 10 10 20 20 OD 1 1 2 2 4 4 5 5 20 20 O C 1 1 2 2 4 4 5 5 10 10 20 20 1 1 2 2 1 1 20 20 1 1 2 2 1 IN NG 1 5 5 2 2 2 2 3 5 NIG 2 21 I 1 1 1 20 20 1 20 20

Determine which statement matches each inequality x 10 x 10 x 10 Literal Inequalities Review 10 a Carrie can own up to 10 fish b Carrie must work at least 10 hours c Carrie gets a discount until she is 10 years old d Carrie is working to earn more than 10

5 Given f x 9x5 6x 7x 5 how many sign changes are there in the coefficients of f x Choose the correct answer below O 2

2 9 Solve x 6 x 4 Step by Step Solution Step 1 Determine the domain of the variable in the rational equation

The diagram shows a simplified distance time graph model of Jordan s and Clark s performances in a 200 m race Jordan allowed Clark an advantage of a certain distance a b c 200 Distance m Clark Jordan 10 Time s 20 30 What was the advantage in terms of distance given to Clark Find Jordan s speed in the race When and where did Jordan overtake Clark d Who won the race How much faster in seconds was the winner