Quadratic equations Questions and Answers

Question 1 4 Match each polynomial with a factoring technique If none of the techniques can be used to factor the polynomial select none Factor by grouping Difference of Squares Perfect square trinomial 8zy 4y 10z 5 16m 40mn 25n 64d 9 0 261 C 0 n 00 ODDE n None 0000

Use the dropdown menu to indicate whether each equation below has zeros at 1 2 a 82 2 b 2x 3 0 c 5 32 2 1 1 d 12x 5 2

Solve the following polynomial by factoring d d 12 Font Size S A A BIUS x x M 04 40 111

Question 1 8 The polynomial a 7a 2ab 14b can be factored into a 7 and O a 2b Oa 2b O2 a 26 Oa a 2

Question 1 10 Factor completely 27 0 y 3 o y 3 y 3y 9 y 3 y 3 o y 6 y 12y 9

Question 1 11 Determine the sum of the solutions to 27 5z 12 0 O E 2 0 4 5 2

Factor completely 7y 2ry 10r 35 y 5 2x 7 y 7 2x 5 2x 7 Oy 7 3x 5 3x 5 O not factorable

Write each of the following statements using symbolic language 1 When you square five times a number you get three more than the number

3 1 Graphing Quadratics 2 Homework CMR Graph each equation 1 y x 8x 12 3 y x 6x 10 Ay 0 5 1 5 2 2 5 3 5 5 y 2x 12x 22 Ay 12 16 8 X X X Y Y Y 2 y 2x 4x 5 Ay 543 21 4 y 2x 4x 3 Ay 3 4 9 8 7 6 5 6 7 6 y 2x 16x 31 8 x 13 12 1 X X

Solve each system by substitution 7 y 2x 16x 30 9 8 7 6 5 433 2 1 y x 4x 5 3 b 41 11 y 2x 16x 28 Ay 0 5 15 25 3 5 55 x X X X Y Y Y 8 y 2x 8x 5 34024 10 y x 4x 3 AY 35 25 13 05 0 3 1 5 12 y 2x 4x 49 X X X

Solve each system by substitution 7 y x 8x 12 9 y 2x 16x 30 Ay 11 y x 4x 2 25 1 5 05 0 5 X X X Y Y 8 y 2x 12x 14 Ay 10 y x 6x 11 6 5 12 y x 4x 2 1 05 0 5 1 5 AM X X

Graph each of the following Use one coordinate system for each problem 9 a y 2x b y 2x 3 c y 2x 5 1 10 a y 3 b y x 1 11 a y x b y x 2 c y 3x 3 c y x 2

NAME Chian louds Solve each system by substitution 13 y x 2x 3 n y P 15 y x 8x 13 41 17 y 2x 4x 5 Ay 20 HA H 4 0 5 0 5 15 25 45 4 36 x X X X Y Y DATE 14 y x 4x 2 AY 21 114 CC 65 15 25 16 y 2x 8x 9 Ay 18 y x 2x 3 3 f 6 5 0 5 15 435 PERIOD X X X Y Y

17 0 00000137701 x 135307 2596

Graph each equation 1 y 2x 4x 4 Ay 3 y x 6x 12 5 y 2x 16x 36 A 4 3 2 1 123456x X X X Y Y Y 2 y x 2x 1 15 05 05 E 4 y x 2x Ay 3 5 25 IS 05 0 5 6 y 2x 16x 34 AY T x X X X Y Y

Solve each system by substitution or elimination 13 3x 8y 22 x y 118 3x 22 6 15 11xx 66 6 y 2x 6 x 3y 17 6 y 11 6 925 3 2x 6 7 x 6 18 17 SX 18 12 the 117 118 7 8 Sx 35 x 29 17 5x 7y 3 7x 8y 15 40x 1869 24 44x 30x 105 dx 81 4 8 x 4 y 2 6 8 9 14 8x 6y 10 6x 7y 15 16 18 sej y 3 45 29 3 45 45 7x y 14 14x 4y 28 74 42 7 y 6x 5 2x 4y 20

3 Tyler has three dogs of different weights Max Daisy and Charlie 3 Daisy weighs as much as Max Charlie weighs 8 Daisy Who weighs the least How do you know as much as

7 STEM Connection Hannah is measuring three sheets of metal Sheet A is 1 times as long as Sheet B Sheet C is 2 times as long as Sheet A Order the sheets from last longth to groat et lang

9 A linear quadratic system contains the quadratic function y 3 x 5 6 and a linear function y 7 5 How many times will the line intersect the parabola 3 2 5 2 5 6 2 C 0 A B 1 D 3 2 52 52 25 6 3 2 62 25 6 intercepts 2 and 3 that goes None of the above v 2 31

Simplify the following expression 5 5 5 5xy 13 4 x y 3 5x y4 Simplify your answer Type an exact answer using radicals as needed

Type your answers in all of the blanks and submit X 2 Fill in each blank with the appropriate word a A rational expression is a quotient of two Write your response here b A number is a restriction on a rational expression if the number makes the denominator of the rational expression Write your response here

Arrange the steps to solve the equation in the correct order 2 6 x III E III Drag and drop options into correct order and submit For keyboard navigation SHOW MORE HIX 1 2x 6 x 2x x 6 0 2x 30orx 2 0 2x 3 x 2 0 2 2 X 3 orx 2 X

Fill in the blanks with the appropriate numbers or expressions related to the following equation X 2 2 X 4 X 3 x 7x 12 a The restrictions on the variable are smaller number in the first blank Type your answer here If not enter none Write your response here and Type your answer here b When you solve the equation do you get any extraneous solutions If so enter the alue of the extraneous sIlution in the blank c The solution set of the equation is Write your response here Enter the Enter the solution set notation If there is more than one answer separate the solutions by a comma and list the numbers in order from smallest to largest

Use the laws of exponents to simplify Do not use negative exponents in your answer 4 5 0 2 2 5 Lo n Simplify your answer Type exponential notation with positive rational exponents

X X Solve the equation Enter the solution set in the blank Write the solutions separated with a comma in order from smallest to largest with no spaces 2 XIN X 4x 6 Solution set 6 2 You are incorrect X

4 For this quadratic function y 3 x 1 7 2 b 4ac 0 b b 4ac 0 a C b b 4ac 0 sacs d 6 4ac 0 v x 111 7

What equation results after clearing fractions from the equation XI W ro a Select an answer and submit For keyboard navigation use the up down arrow keys to select an answer 10 4x C d 2 N b 3 10x 2 12 10 8x 12 10x2 3 10x 8x

According to the Pew Research Center for Journalism and Media the estimated circulation of weekday newspapers in millions in the United States can be approximated by the formula C 0 0166x 1 2109x 41 708 where X is the number of years after 1940 According to the formula in what year would the circulation of weekday newspapers be 0 million Round to the nearest year Source https www journalism org fact sheet newspapers Type your numeric answer and submit

Fill in the blanks with the appropriate information to solve the equation x 14x 10 5 a To solve the equation by completing the square first add b This produces the equation x 14x Type your answer here Type your answer here c The number that completes the square for the equation is Type your answer here d Add this number to each side and simplify Write your response here e The solutions of the equation from smallest to largest are Type your answer here Type your answer here to each side Type your answer here and Opon

Write the radical expression as an exponential expression 3xy 3xy Use integers or fractions for any numbers in the expression Type your answer using exponential notation

Find the real solutions to the equation 192 3h6 h Simplify your answer Use a comma to separate answers as needed

Write the radical expression as an exponential expression 4xy5 4 4xy5 Use integers or fractions for any numbers in the expression Type your answer using exponential notation

Write the expression in radical form 71 b b C

Solve the equation by filling in the blanks FIND ALL REAL SOLUTIONS 524 405 X

9 i Listen Compare the graphs Find the value of h k or a 96 a z f x 2 The graph of g is a vertical shrink by a factor of Previous 5 10 of the graph of f a 11 12 13 Next

H y f x 000

Select all the toolkit functions below that are discontinuous Quadratic function Absolute value function Logarithmic function Rational function

Solve the following system of equations algebraically y x 14x 27 y 3x 1

Solve the equation and check your sol If y 4 what is the solution 2x y 0 H 123 f E ABC

5 Solve the equation and check yo If y 13 what is the solution x y 0 Type a response

Solve the equation and check your solution If y 8 what is the solution 2x 10 y 0 Type a response and check your solution It

7 Solve the equation and check your solutio If y 6 what is the solution 00 5x 4 y 0 Type a response Solve the equation and check your solution

Solve the equation and check your s If y 20 what is the solution 2x y 0 Type a response

After door to door canvassing census workers determine the number of unoccupied homes The table shown to the right lists the number of homes in millions that were unoccupied in four census years Answer questions a through c Year x 1965 0 1975 10 1985 20 1995 30 a Use a graphing calculator to fit an exponential function to the data where x is the number of years after 1965 y Type integers or decimals rounded to six decimal places as needed Number of Unoccupied Homes in Census in millions 5 8 7 3 9 1 14 3

Country A has an exponential growth rate of 4 49 per year The population is currently 4 039 000 and the land area of Country A is 37 000 000 000 square yards Assuming his growth rate continues and is exponential after how long will there be one person for every square yard of land This will happen in year s Round to the nearest integer

In a town whose population is 4000 a disease creates an epidemic The number of people N infected t days after the disease has begun is given by the function 4000 N 1 1 17 16 0 4 Graph the function Find the number of people initially infected and the number infected after 11 days Choose the correct graph OB a Q G All graphs are 0 20 0 5500 Xscl 1 Yscl 500 How many are initially infected with the disease t 0 people Round to nearest integer or whole person Q Q L

Solve the equation and check your solution It is possible that there is NO SOLUTION If y 13 what is the solution x y 0 Type a response

6 Graph f x and g x on the set of axes below f x X x 4x 3 x 1 g x x

Mic 1 Aare pa 2 HAHT 1 P m p ne 8600 325 576 x 42 165 220 480 2 P n e p 5 4a a 6 3 3 11 12 7 8 a 6 6 7 4 2 3 9m 7m m 8 m 16m 64 49 a 27 4 Y 9m 65 8m 64 m 64 5 x 7x 4 0 x m 8 16 2 x 3 12 x x 3 x 3 x 9x 3 x a 3 1 7 15 2 a 27a a 27a 40 a 2 2 a 3a 9 16 a 8 x x 1 x x 1 6 1 4 a

d No the polygon is not regular It is equiangular but it is not equilateral No the polygon is not regular It is neither equilateral nor equiangular 94 94 Yes the polygon is regular It is both equilateral and equiangular No the polygon is not regular It is equilateral but it is not equiangular No the polygon is not regular It is equiangular but it is not equilateral O No the polygon is not regular It is neither equilateral nor equiangular X