Quadratic equations Questions and Answers

question Use the Mathematician s Plan to answer each question Show all work and attempt every 1 Determine the coordinates of each point below E 10 9 0 A 70 6 5 B 2 2 3 4 5 6 y 8 G H 2 State the coordinates of each of the points below YA A 7 6 B 5 C 4 3 D 2 E 1 F A 7 6 5 4 3 2 1 0 2 3 40 5 6 7 F 1 E 2 3 B 4 A B C D E F G H 1 5 6 D 7 x

Put the function P 7 1 2 in the form P Poekt NOTE Round your answer to four decimal places if required P

A turbo prop plane flying with the wind flew 1400 mi in 5 h Flying against the wind the plane required 7 h to travel the same distance Find the rate of the wind and the rate of the plane in calm air

F The position of a particle moving along a coordinate line is s 25 4t with s in meters and t in seconds Find the rate of change of the particle s position at t 6 sec The rate of change of the particle s position at t 6 sec is Type an integer or a simplified fraction m sec CL

Use the quadratic formula to solve the equation 2x x 1 TER The solution set is Type an exact answer using radicals as needed Type your answer in the form a bi Use a comma to sep answers as needed

Describe how the graph of the function can be obtained from one of the basic graphs g x x 5 7 Start with the graph of h x x Shift it units Then reflect it across the and shift it units

Given that f x x 6 match the function g with a transformation of f g x x 4 6 What is the transformation O A g x f x 4 OC g x f x 4 O E g x 4f x O B g x f 4x O D g x f x 4 OF g x f x 4

The heights of a ball after t seconds when thrown straight up with an initial speed of 70 feet per second from an height of 5 feet can be modeled by the equation s 16t 70t 5 a When will the height of the ball be 40 feet b When will the height of the ball be 70 feet c Will the ball ever reach a height of 130 feet a The height of the ball will be 40 feet after approximately seconds Use a comma to separate answers as needed Round to the nearest tenth as needed b The height of the ball will be 70 feet after approximately seconds Use a comma to separate answers as needed Round to the nearest tenth as needed c Will the ball ever reach a height of 130 feet Choose the correct answer below O A Yes because both solutions of the equation when s 130 are irrational O B No because one of the solutions of the equation when s 130 is negative O C No because both solutions of the equation when s 130 are rational

Zero is the smallest integer True False

Use a vertical format to find the product x 3x 6 4x 8

Ive the following equation using the quadratic formula 2 5x 3x 2

To help with her retirement savings Jina has decided to invest Assuming an interest rate of 3 47 compounded quarterly how much would she have to to have 147 200 after 20 years Do not round any intermediate computations and round your final answer to the nearest dollar If necessary refer to the list of financial formulas sm

Solve 8 sin n 7x x 3 for the four smallest positive solution

A C b 2 21 30 O C sin 21 30 OD sin 21 30 cos 21 30 a C 6 What is the length of c in the right angle triangle shown O A sin 21 30 O B 2cos 21 30

For the function below a find the vertex b find the axis of symmetry c determine whether there is a maximum or a minimum value and find that value and d graph the function 2 f x x 4x 5 a The vertex is 2 1 Type an ordered pair using integers or fractions b The axis of symmetry is x 2 Type an equation Use integers or fractions for any numbers in the equation c Does f x have a maximum or a minimum value The parabola has a minimum value The parabola has a maximum value The minimum maximum value is Type an integer or a fraction 10 8 6 4 Ay 10 8 6 4 2 2 4 6 8

f x 5 4 3 2 N 1 4 3 2 1 0 1 2 1 2 ge of the piecewise function above 3 4 X

7 4 1

2x 8 x 2 f x x 3 2 x 3 x 3 Evaluate f 3 in the piecewise function above Evaluate f 2 in the piecewise function above Evaluate f 1 in the piecewise function above Dovers x 3

Use the graph of the quadratic function f x a x h k to find the vertex axis of symmetry and the minimum or maximum value of the function The vertex is Type an ordered pair B 10 Ay V 6 10 10 G

Consider the quadratic function below and a find the vertex b find the axis of symmetry c determine whether there is a maximum or a minimum value and find that value and d graph the function f x x 14x 48 a The vertex occurs at Type an ordered pair using integers or fractions 10 8 6 2 8 6 4 2 2 4 64 8

9 Graph the system of inequalities Show at least two points for each inequality Lesson 1 08 E and and and y 2 5x y x 4 1 y s 3 x 10 8 6 4 2 10 8 CO 6 4 2 24 6 8 2 nch 4 6 8 10

1 8 5 4x 6w 2 9 th 8b 3 7f 6 5b 2 8 20 X 4 w 9 b q k 4 4 3x 7 6 5c 5 8 6 55 92 7 7 66 h 3 f 7 C 7 X 9 2 9 S 3 h 7 b 7 r s b 6

By completing this practice test you will earn 10 points All of your practice tests for the semester total to 10 of your grade in this class You MUST do the following to earn the points Show all work answers and explanations that we go over in class Handwrite everything no typing Submit as one document Word or PDF 1 What is the solution to the system of linear equations Lesson 1 02 6x y 14 2x y 2

Use the table below to write the traditional Chinese numer Hindu Arabic numeral Hindu Arabic Numerals 1 2 3 5 5 Traditional Chines Numerals 10 B 14 K to 40

olve the problem A club has 42 male members and 35 female members If the club is t have a contest where there are all male and all female teams competing what is the most members a team can have All teams must be of equal size and everyone must be on a team O 210 07 O 42 35

Add in the indicated base 30 five 343 five O 1440 five O 1240 five O 124 five

Solve the problem A movie theater has two screens and shows its movie continuously A 30 minute documentary is shown on one screen A 120 minute feature is shown on the other screen If both movies begin at noon how many minutes will pass before both movi begin again at the same time O 240 minutes O 120 minutes O 150 minutes inutes

Write the Roman numeral as a Hindu Arabic numeral XLVI 0 46 O 154 O 165 54

Note Recall if g a b R is an integrable vector valued functions with components 8 828 then 18 x dx 18 4 8 1 dx Equivalently written in the columnal 8 x dx a form we have jg x dx je x dx We will use these notations in this article Example 1 Obtain approximate solutions upto of the following initial value problem 2x 3y x 0 1 Thus Next dx dt dy dt Solution js 1 de 8 x dx 1 y y 0 2 We have x t 1 2 500 1 12 400 3 00 1 18 8 1 y 1 2 s y s ds 2 s 2 ds 2 21 2 21 1 2 2 81 1 1 2x s 3y s ds 1 8r 1 y 1 2 s y s ds 2 2 s Y s y 1 ds 2 2 3x 2 ds 13 21 2

10 Objective function 4x 5y Constraints r 0 120 2x 2y 10 x 2 6

12 1919 up

Use the following right triangle to find the functions tanA cosA and cscA C 3 8 B

If 0 3 4 sec 0 equals csc 0 equals tan 0 equals cot 0 equals use the unit circle to find exact values for the following

Given that f x 3 what is the limit as a O 3 0 0 O 00 Does not exist

Write an equation in y mx b form for the linear relationship shown in the table Servings 4 8 10 Cups of Pasta for Diabetes Patients The equation in 1 2 132313 3 DO NOT USE ANY SPACES between variables constants equals signs and operation signs For example DO NOT enter y 2x 1 DO ENTER y 2x 1 Put parentheses around constants that are fractions like this y 2 3 x 1 2 You may use decimals IF the decimal values are exact You cannot use 33 for 1 3 because it is not exact To write your equation use the variables s number of servings c s cups of pasta Yold

1 2 3 4 LO 5 Graph the solution to the inequality on the number line 5x 10 15 6 4111 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 7 X

1 Solve 2 3 4 w 17 5 If all real numbers are solutions click on All reals If there is no solution click on No solution 11 N No solution 5 and 00 IND or 6 All reals

1 Question 2 of 11 1 point Question Attempt 1 of Unlimited Solve for w W 2 0 3 2 w 6 If there is more than one solution separate them with commas If there is no solution click on No solution 4 010 5 X 0 0 6 No solution S

5 123 47 5 5 1

Draw a graph for the description The vertices are A B C and D The edges are AB BC CD BD and BB Choose the correct graph below OA A B O B A D O C Co

K How wide is the chasm between what men and women earn in the workplace According to a 2015 analysis from a national women s group women lose 435 049 over the course of a career because of the pay gap The bar graph to the right Average Yearly Earnings in the shows the average earnings in the United States for men and women at ages 24 and 60 This exercise involves the graphs of by Gender Age models for the data shown in the rectangular coordinate system to the right Complete parts a through c below 70 60 Men 50 Women This question 1 point s possible W x Use integers or decimals for any numbers in the expression Round to two decimal places as needed Average Yearly Earnings 1000s M age 36 thousand Type an integer or decimal rounded to one decimal place as needed Next find the average yearly earnings for women at age 36 W age 36 thousand Type an integer or decimal rounded to one decimal place as needed 40 30 24 Age 60 Average Yearly Earnings 1000s 70 60 30 62 50 0 26 40 30 20 10 a Use the two points for men shown on the graph to find a function in the form M x mx b that models average yearly earnings for men x years after age 24 M x Use integers or decimals for any numbers in the expression Round to two decimal places as needed b Use the two points for women shown on the graph to find a function in the form W x mx b that models average yearly earnings for women x years after age 24 0 0 22 Submit qu Men 30 38 Women 0 10 20 30 40 50 Years after Age 24 c Use the models in parts a and b to find the average yearly earnings for men and women at age 36 How are these values shown on the graphs of the models for the data What is the difference between earnings for men and women at that age Start by finding the average yearly earnings for men at age 36

1 5 and parallel to x 2y 5 X 9 a The equation of the line in slope intercept form is y 2 2 Type your answer in slope intercept form Use integers or fractions for any numbers in the equation b The equation of the line in standard form is Type your answer in standard form

Simplify 5x 2x 5 3x 3x 1 O 2x 5x 4 O 2x 5x 4 O 8x 5x 4 O 2x x 6

The monthly cost of a certain texting plan is given by the function y 0 07x 14 95 where y is in dollars and x is the number of texts sent in a month Find and interpret the slope and y interce the linear equation A m 14 95 The number of texts sent in a month increases 14 95 for every dollar spent b 0 07 The number of texts that can be sent when x 0 is 0 07 B m 0 07 The number of texts sent in a month increases 0 07 for every dollar spent b 14 95 The number of texts that can be sent when x 0 is 14 95 OC m 14 95 The cost of the texting plan increases 14 95 for every text sent b 0 07 The cost of the texting plan is 0 07 if no texts are sent for the month O D m 0 07 The cost of the texting plan increases 0 07 for every text sent b 14 95 The cost of the texting plan is 14 95 if no texts are sent for the month C

ork 7 1 Evaluate the function at the given value of the variable f x 3x 5x 3 a f 3 b f 4 a f 3 39 b f 4

Plot the ordered pair 5 9 on the rectangular coordinate plane Plot 5 9 Next question 10 10 8 8 2 4 6 8 Ay TO E G

Plot the intercepts to graph the equation x y 8 Use the graphing tool to graph the equation Use the intercepts when drawing the line If only one intercept exists use it and another point to draw the line Click to enlarge graph O Points 0 of 1 Ay 10 8 6 2

Watch the video and then solve the problem given below Click here to watch the video Calculate the slope between 3 4 and 4 2 The slope is Type an integer or a fraction

Complete the following proofs 11 Given AB is the bisector of 4CAD Prove x 9 Statements 1 AB is the bisector of ZCAD 2 ZCAB ZBAD 3 m CAB m BAD 4 7x 2 5 x 4 5 7x 2 5x 20 6 D 7 F Reasons 1 Given 2 A 5 C 7x 2 6 E 7 G A B 3 angles have equal measures 4 B 5 x 4

14 Given m4PMN mARBC Prove mAABR m4PMN m4ABC B A C