Quadratic equations Questions and Answers

15 If a garden box has dimensions x by x feet and an area in square feet equal to two times the perimeter in feet what is the value for x that satisfies the requirements Hint The box is a square X feet

12 Factor the following binomial x 16 Factored binomial

8 Given six consecutive integers with a sum of two times the second number write an algebraic equation for this situation n n 1 n 2 n 3 n 4 n 5 2n O n 1 6 2n n n 1 n 2 n 3 n 4 n 5 2 n 1 6n 6 2n

Factor the following trinomial y 5y 36 Factored trinomial

Solve the following quadratic expression by fact More than one answer may be correct Check al c 49 0 7 7 8 8 0

f a garden box has dimensions by x feet and a quare feet equal to two times the perimeter in fe the value for x that satisfies the requirements x 2 feet x 8 feet x 4 feet There is not enough information in the proble

2 ve the quadratic equation by factoring til all possible answers You may check your sol graphing it 16x 54x 7 Don t forget to set all terms on one side and equation equal to zero before beginning to fac Hint the factors begin like this 2x 8x More than one answer may be correct mark 0 12 2 0 1 01 01 8 None of the above

factoring first Select all possible answers a 5a 6 0 3 0 2 02 0 3

Find a quadratic function f having the graph shown The quadratic function representing the graph shown to the right is given by f x 10 B 6 10 8 6 4 2 2 4 6 B 0 0 24 6 2 IN

A toy rocket is launched from the top of a building 87 feet tall at an initial velocity of 207 feet per second a Give the function that describes the height of the rocket in terms of time t b Determine the time at which the rocket reaches its maximum height and the maximum height in feet c For what time interval will the rocket be more than 471 feet above ground level d After how many seconds will it hit the ground a The function that describes the height of the rocket in terms of t is s t

For the quadratic function f x x 3 2 determine the largest open interval of the domain a over which the function is increasing and b over which the function is decreasing a The largest open interval of the domain over which the function is increasing is Type your answer in interval notation

Using a graph find all the roots of the quadratic 2x 3x 3 rounding to the nearest tenth 0 7 0 2 2 2 0 4 8

For the polynomial function a list all possible rational zeros b find all rational zeros and c factor f x f x 6x3 31x 25x 12 a Determine the possible rational zeros for f x Choose the correct answer below 1 OA 1 2 3 4 6 1 3 2 OB 4 2 3 1 1 1 2 4 3 2 3 6 3 3 2 O c 1 2 3 4 6 12 7 1 1 1 2 4 3 1 1 2 3 6 3 3 2 1 OD 1 2 3 4 6 12 2 1 3 H 160 1 1 Nim W A 4 3 1 3 2

Graph the quadratic function f x 3x 24x 45 Give the a vertex b axis c domain and d range a The vertex is Type an ordered pair

3 Graph the following on a separate sheet of pape or on a graphing calculator or computer Use y find the solution s to the problem x 7x 18 More than one answer may be correct mark a 18 0 12 9 01 0 2

To graphically solve the quadratic equation x 2x 10 6 Set the equation y x 2x 10 equal to Then find the roots of the graph Use the quadratic formula letting a 1 b let y x 2x 10 and y2 6 Find the points at which they intersect all of these are practical ways to solve the qua

Use synthetic division to decide whether the given number k is a zero of the given polynomial function If it is not give the value of f k f x x3 5x 3x 3 k 1 i Is 1 i a zero of the function Select the correct choice below and if necessary fill in th answer box to complete your choice The given k is not a zero of the polynomial function f 1 i Simplify your answer Express complex numbers in terms of i B The given k is a zero of the polynomial function O A

If a garden box is x by 4x and the area of the box in square feet is equal to twice the perimeter in feet what is the value for x that satisfies these requirements Check your answer by graphing X

The table shows the percent of workers that stayed in their chosen field The data are modeled by the following quadratic function where x 0 corresponds to 1990 and f x is the percent f x 0 14x 1 30x 46 Predict the percent of workers that stay at their job in the year 2008 Year 1990 1992 1994 1996 1998 2000 Percent c Workers 46 0 44 0 43 0 43 1 44 9 47 0 Approximately of workers are predicted to stay at their job in the year 2008 Round to the nearest tenth as needed

raph the following equation on a separate sheet of paper on a graphing calculator or computer Use your graph t nd the solution s to the problem 9x 9 More than one answer may be correct mark all correct a 1 7 3 3 1 1 1 13 14 17

A piece of cardboard is 2 4 times as long as it is wide It is to be made into a box with an open top by cutting 3 inch squares from each corner and folding up the sides Let x represent the width in inches of the original piece of cardboard Answer the following questions X 3 3 3 3 a Represent the length of the original piece of cardboard in terms of x Length in Use integers or decimals for any numbers in the expression

Graph the quadratic function f x x 6x 11 Give the a vertex b axis c domain and d range a The vertex is Type dered d nair

8 Graph the following quadratic equation and find the solution by interpreting the graph State how many solutions there are 0 1 or 2 x 4x 5 X Number of solutions

4 John wants to design a garden space behind his home He wants exactly 300 square feet for his use He has exactly 80 linear feet of fence with which he can enclose the garden space What would be a good dimension for the length and width of his garden space Answer in the space provided

3 Graph the following quadratic equation and find the solution by interpreting the graph State how many solutions there are 1 2 or none x 4x 5 0 1 02

You decide to buy a house that costs 220 000 and repay the loan with monthly payments over the next 30 years The interest rate is fixed at 4 75 What will your monthly payments need to be so the loan is completely paid off at the end of those 30 years

5 If George had a square garden behind the house and each side was 2 feet longer than the side of the house we ll let the length of the house be x feet since we do not know the exact length of the house what would be a good expression for the area of the garden

Choose whether the expression is a result of multiplying conjugates together squaring binomials or neither 49x 84x 36

city is building a new park and issues bonds to raise money to build it You obtain a 1 000 bond that pays 5 interest annually that matures in 6 years How much interest will you earn This is the same question as Question 11 Upload your work showing the steps you used to solve this problem Don t forget your dollar signs in your final answer Round numbers at the very end

account paying 6 interest Assume that the account is compounded with the same frequency as we make deposits unless stated otherwise How much money will be in the account in 2 years Write down this question in your notebook You will need it for another question

Nine and one half less than four and one half times a number is greater than 62 5 Which of the following represents th solution set of this problem O 16 00 O 16 00 O 0 16 O o 16

What is the rate on an investment that triples 9465 in 35 years Assume interest is compounded monthly O 3 9 O 3 1 O 2 1 2 6

Z NH INI represent the given graph

Write an absolute value function to represent the given graph

In a beheaded cone placed a sphere so touch the pedestal the top and the perpendicular space of beheaded cone Area of the top of the beheaded cone is less than area of the pedestal Find the ratio of the beheaded with sphere volume a a 1 2 a a a 2 2 a a a 3 2 a a a 4 2 a

Enter your answer in general form INW 3 4

Question Determine the equation of the parabois whose graph is given below Enter your answer in general form 7 6 5 34 5

The graphed function is a transformation of the the original functions Which equation describes the graph y 5 4 3 24 1 5 4 3 2 1 0 2 3 4 51 Of x 2 2 2 Of x 2 2 Othe Jo 2 2 3 4 5

Problem 3 Use long division of polynomials to divide P x 2x x 1 by D x x x 1 and express P in the form P x D x Q x R x

3 Write the equations for the transformed graphs dotted 5 5 X X 5 5

Determine if the function is quadratic If it is determine if the graph is concave up or concave down Determine if the vertex of the graph is a maximum point of minimum point y x 6x 6 Is the function quadratic Yes No

polynomial graphed below f x 5 4 3 2 1 54 32 2 2 3 S 2 3 4 5 IT

Use the shell method to find the volumes of the solids generated by revolving the shaded region about the indicated axes a The x axis b The line y 4 c The line y 5 d The line y 5 8 a The volume is cubic units Type an exact answer using as needed N WA 4 3 1 X 16 2 N 1 4 4 4

Task 1 Sort the following cards into matched sets of an inequality a graph of its solution and 3 the solution set written in interval notation A B C D E F G H I 3 1 2 x x 4 2x 5x 3 x 2 x 3 x 8 X 2 3 x x 1 x x 2 0 2 1 x 4 x 1 3x 1 x 4 21 x 1 x 6x 9 0 x 3x 10 1 x 22 R 3383216123456 S T 3343290 1 2 3 4 5 6 U V W X 3543210 1 2 3 4 5 6 Y Z Solutions write the letter number label only Inequality Graph 23456 23156 Solution 1 2 3 4 5 6 7 8 9 1 3 U 3 00 0 3 U 8 00 4 1 U 2 00 4 U 2 00 0 3 U 1 4 2 U 0 4 2 U 1 00

RC1 x 2 RC3 x 2 RC5 x 2 a 12 b c 12 12 f e 12 10 d 12 12 10 10 10 10 10 8 8 8 8 8 8 6 6 6 6 6 6 4 4 4 4 4 4 2 2 2 2 2 graph of the solution RC2 x 22 RC4 x 2 RC6 x 2 0 0 0 0 0 0 2 2 2 2 2 2 4 4 4 4 4 4 6 8 6 6 6 6 6 8 8 8 8 8 10 10 10 10 10 10 12 12 12 12 12 12 Select the correct graph for each inequality Graph of the solution Inequality RC1 x 2 RC2 x 22 RC3 x 2 RC4 x 2 RC5 x 2 RC6 x 2

Given f x and g x k f x use the graph to determine the value of k 0 5 O 150 g x 10 f x 10

Consider the graph shown below 4 absolute minimum 2 x y 200 150 100 50 50 A 100 150 200 6 250 If the complete graph of the function is shown estimate the absolute maximum and absolute minimum absolute maximum x y 200

2 The percent grade of a road is the ratio of vertical rise Ah to the horizontal change in distance d expressed as a percent A road is found to have a percent grade of 3 5 a What is the horizontal distance d with a vertical rise of 980 m Ah Round to whole number in meter b For 100 km horizontal distance d for a stretch of this road what will be the vertical rise Ah Round to whole number in meter 4 marks i B Ah

Give the equation in factored form of the polynomial function graphed below Note Zeros will not have multiplicity greater than 3 Use the y intercept to help you determine the leading coefficient 0 A

1 Multiply the following binomials 5b y 4b y O206 9by y O206 1by y O206 4by y 208 5by y