Quadratic equations Questions and Answers

Find a formula for the inverse of the following function if possible A x x 5 5

Let f x 7x 2 and g x 4x 5 Find f g x f g x fg x and f g x Simplify your answer x Give the domain of each

Show that 3 5 27 is a solution of the equation x 7x 16 25 0 To show that 3 5 2i is a solution of the equation x2 7x 16 25 0 the first step is to substitute 3 5 2i for x in the equation x 7x 16 25 0 Perform the substitution 0 35 27 2 7 3 5 27 16 25 Do not evaluate What is the most useful next step OA Take the square root of both sides of the equation to clear the exponent OB Multiply both sides of the equation by the complex conjugate of the imaginary number in parentheses c Expand the right side of the equation D Divide both sides of the equation by the constant 16 25 Apply the next step 0 12 25 7i 7i 4 24 5 14 16 25 Do not combine like terms Now combine like terms 4

Let the graph of f x be given below Find the formula of f x a polynomial function of least degree 18 Click on graph to enlarge f x help formulas

Question 3 Let f x 22x 189x 248r 21 According to the rational roots theorem which of the following does NOT represent a possible pair of rational roots of this polynomial 7 11 21 21 22 11 1 3 3 22 70 Question Help Message instructor 1 11 3 21 22 2 O 3 11

The graph of 2x 5y 10 Is shown on the grid 30 A 0 5 B 5 0 C 2 5 D 5 2 Y 10 31 enn M 15 9 Which ordered pair is in the solution set of 2x 5y2 10 a X

8 Jim and Joe are brothers Joe is 30 older than Jim If Joe is 39 how many years older is he than Jim 130 39

Find a polynomial of degree n that has the given zero s There are many correct answers x 7 n 2 f x

4 Nicole spends 15 minutes completing her math homework and looking over her notes each night However after her first quiz she isn t happy with her grade She decides to increase the amount of time she spends on math by 75 How many minutes does she now spend working on math each night

3 Kayla calculates that she ll spend 75 more money if she orders takeout for all of her din ners for a week than if she cooks the meals herself If she would spend 60 to cook for herself how much would takeout cost

4 Last year the budget for the Winter Dance was 500 This year it increased by 20 How much was the budget for the dance this year a 400 b 520 A 600 d 1000

2 Ms Hollis decides to let her students vote on whether the final project should be completed independently or in groups 50 more students wanted to complete the project in groups than wanted to complete the project independently If 60 students wanted to complete the project in groups how many people wanted to complete it independently a 10 b 20 C30 d 40

2 John is training for a bike race Over his training program he increases his weekly mileage by 25 At the end of his training program he bikes 243 miles in a week How far was he biking at the beginning of the week

Score 2 10 Penalty none Question Answer the questions about the following polynomial Answer Attempt 1 out of 2 The expression represents a is 10 6 and the leading coefficient is Submit Answer polynomial with Watch Video terms The constant term is Show Examples 0 the leading term

What is the solution set of the equation 2 9 Note q 0 1 O 1 4 o 4 4 2 O 2 4 q 4 9 1

QUESTION 1 2 points FIND The Domain of the function f x 2 T 9 7x

Heather wrote this solution to solve for x Which statement is true 1 is an extraneous solution because it creates a 0 in the denominator O 5 is an extraneous solution because it creates a 0 in the denominator O There are no extraneous solutions O Both 1 and 5 are extraneous solutions because they create a 0 in the denominator 6 x 9x 20 6 x 5 x 4 x 4 x 5 x 4 x 5 x 4 1 x 1 X 4 X 5 1 x 1 X 4 x 5 H H x 5 x 1 x 4 6 x 5 x 4x x 4 6 0 x 4x 5 0 x 5 x 1 x 5 or x 1 6 x 5 x 4 x 5 x 4 Factor Multiply by the LCD Simplify Simplify Combine like terms Zero Product Property Solve for x

Use the remainder theorem and synthetic division to find f k for the given value of k f x x 7x 11x 1 k 5 f 5

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 x 4x 8x 15 k 3 Is 3 a zero of the function Select the correct choice below and if necessary fill in the answer box to complete your choice O A OB The given k is not a zero of the polynomial function f 3 Simplify your answer The given k is a zero of the polynomial function

For the following polynomial function use the remainder theorem to find f k f x 3x5 9x 19x 40 k 2 f 2 Simplify your answer

Express f x in the form f x x k q x r for the given value of k f x x 7x 13x 6 k 2 f x

Write an equation any form for the quadratic graphed below 6 5 4 2 6 S 4 3 2 2 3

3 2 2C Understand the relationship between zeros and factors in polynomials NM PT AT Let g be a polynomial function of x where g x 1 If x 3 is a factor of g what is the remainder of g x x 3 f x Write an equation for g as the product of linear factors g x 2x 5x 28x 15 3 4 Let f be a polynomial function of x where f x x 8x 20x 16 We know that f 2 0 f 0 16 and f 2 96 Use that knowledge to re write f x in factored form The input of 2 produces an output of 0 What other input s produce an output of 0 How do

2 Use the expression to answer the question x y 8 x 3 Y Which of the following answer choices is the simplified from of the given expression 1 A x3y x yl g

Write an equation any form for the quadratic graphed below 6 5 3 6 5 4 3 2 4 2 3 S A k 16

Which value of x satisfies the equation V5z 10 V2 4 0 A B C D 3 2 7 72 2

7 Write the expression below in simplest form x8 24 A B D a V7

3 What is the solution set for the equation 56 x x A 7 8 B 7 C 8 7 D 7 7

The population of owls in an area was estimated to be 200 with a decline rate of 2 each year Which of the following functions model the estimated population of owls in t years Use A p 1 r t OP t 200 0 98 OP t 2 200

Solve for x Be sure to check for possible extraneous solutions and round to the nearest thousandth In x 6 ln 5 2 Ox 22 945 Ox 43 968 Ox 42 945 Ox 32 625

In chemistry logarithms are key to calculating the pH of a solution pH log H In this equation H is the hydrogen ion concentration Fin the hydrogen ion concentration of a substance with a pH of 5 O 10 5 510

Solve the logarithmic equation using properties loga x 10 3 Ox 54 O x 71

5 3 6 2

8 1 8 13 2 O Yes O No O O Yes 2 a Does this table represent a function of x 9 No 3 12 b Does this table represent a one to one function of x 9 c If you answered No in the previous question remove one entry from the table form of an ordered pair so that the new table defines a one to one function Write answer in the form x y in the box below If you answered Yes in the previous question enter NA in the box below

The cost in to make a cupcakes is given by the function of x below c x 3 6x 5 a Express the number of cupcakes that can be made as a function of cost x c b Find the value of x 80 Round to two decimal places if necessary c Interpret the meaning of x 80 O The profit from making and selling 80 cupcakes The number of cupcakes that can be made with 80 O The cost to make 80 cupcakes The profit from making and selling 80 cupcakes

Suppose y is a function of a that does the following steps in order The input is multiplied by 7 Then add 5 Then divide by 8 a Find the rule of the function y b Describe what the inverse function does to its input in order The input is divided by 8 then add 5 then multiply by 7 O The input is divided by 8 then add 5 then multiply by 7 O The input is divided by 7 then subtract 5 then multiply by 8 O The input is multiplied by 8 then subtract 5 then divide by 7 c Give the inverse function as a function of y

Given the function of x below find the inverse function x y x 3 x 1 x y y x

During a road trip the function f t gives the total number of miles driven after t minutes Find f 80 and f 70 using the table below t minutes 30 50 80 70 80 100 120 70 f t miles 70 80 100 120 140 150 Choose all correct statements below f inputs the time spent traveling and outputs the distance traveled Of inputs the distance traveled and outputs the time spent traveling

Fill in each blank so that the resulting statement is true In the following long division problem the first two steps have been completed 2x 3x 6 6x 9x 5 6x 12x 2 The next step is to subtract 2 from which obtains Then bring down and form the new divide

Write an equation for the polynomial graphed below 5 4 3 2 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 Q

7 Dawn Keith and John are all working on a history project Dawn spent 1 2 hours less than 5 times as many hours on the project as John did Keith spent 1 2 hours more than 4 times as many hours on the project as John did If Dawn and Keith spent the same amount of time working on the project how many hours did John spend working on the project

Use the parent function f x 6 and transformation techniques to graph h z 2 3 Also indicate which transformation s is are applied Determine the domain range and horizontal asymptote of h Select all transformations that apply Shift the graph of f 3 units to the left Reflect the graph of f about the c axis Horizontally compress the graph of f by a factor of 3 Shift the graph of f 3 units to the right O Horizontally stretch the graph of f by a factor of 3 Reflect the graph of f about the y axis Vertically compress the graph of f by a factor of 3 Vertically stretch the graph of f by a factor of 3 Shift the graph of f 3 units up Shift the graph of f 3 units down Use the parent function f x b to graph h A

Write the polynomial as the product of linear factors h x x 9x 28x 30 h x List all the zeros of the function Enter your answers as a comma separated list Enter all answers using the appropriate multip

1 Show algebraically that the function f x x 9 is an even function Sketch the graph of f 10 9 8 7 6 5

ne whether fis even odd or nether X 1 1 2

The graph of a linear function f is shown a Identify the slope y intercept and x intercept b Write the equation that defines f The slope is Type an integer or a simplified fraction 1088 2 Ay X

Find the missing digits Enter one digit in each blank a 64 9 6 6 1 b c 16 4 63 1 4 494 586 4 29 8 928 d 0 3 3 927

Match each graph with its equation N 5 4 ABAIX 2 L U 439 2 NO 3 4 a f x immmmm b f x c f x d f x e f x f f x P 2 2 41

Match each graph with its equation 5 4 3 2 125 4 3 HEN SEX P TEL 6 24 12 100 They a f x 3 b f x 3 2 c f x 3 d f x 3 12 e f x 3 37

Solve the following exponential equation 5 321 22 P 625 If multiple solutions exist enter the solutions using a comma separated list