Quadratic equations Questions and Answers

7 On the set of axes below graph the line whose equation is 2y 3x 2

6 Maria orders T shirts for her volleyball camp Adult sized T shirts cost 6 25 each and youth sized T shirts cost 4 50 each Maria has 550 to purchase both adult sized and youth sized T shirts If she purchases 45 youth sized T shirts determine algebraically the maximum number of adult sized T shirts she can purchase

4 The value of x that satisfies the equation 1 6 2 10 x 10 15 3 5 is 4 30

The area of a rectangular wall of a barn is 119 square feet Its length is 10 feet longer than the width Find the length and width of the wall of the barn The width is feet The length is feet

Find f x b Graph f and in the same rectangular coordinate system Use interval notation to give the domain and the range of f and f a Find f x b Choose the correct graph which shows f and f graphed in the same coordinate system OA OB c State the domain and range off and using interval notation Domain of f Range of f 0 Range of f Domain off 0 Oc OD Odu

f Find f g f g fg and Determine the domain for each function g f x 5x 7 g x x 4 f g x What is the domain off g O O O xix is a x x is a real number and x xx is any real number x x is a real number and x 0 f g x What is the domain off g xx is a real number and x O fg x What is the domain of fg O 11 6 x x is a real number and x x x is any real number xx is xlx is a real number and x 3 O x x is a real number and x 0 6 34 x x x is a real number and x 0 7 xlx is a real number and x xlx is a real number and x 4 xlx is any real number

Use interval notation to represent all values of x satisfying the given conditions Y 5x 3 y 4x 2 and y Y2 OA 0 1 OB 1 00 OC 5 OD 1 00

4 x 3 equation a Write the value or values of the variable that make a denominator zero These are the restrictions on the variable b Keeping the restrictions in mind solve the equation 3x 2 x 3 9 a Write the value or values of the variable that make a denominator zero Use a comma to separate answers as needed b Solve the equation ACCES

Graph f x 4 and g x log ax in the same rectangular coordinate system O Q CXS

y varies jointly as x and z y 56 when x 2 and z 7 Find y when x 6 and z 6 V

Britney is solving a quadratic equation Her first step is shown below 2 Problem 3x 1 2 Step One 3x 8 10x 3 2x 3 10x 8 6x 9 Which two properties did Britney use to get to step 1 addition property of equality I II commutative property of addition III multiplication property of equality IV distributive property of multiplication over addition 1 I and III 3 II and III 2 I and IV 4 II and IV

3 A dolphin jumps out of the water and then back into the water His jump could be graphed on a set of axes where x represents time and y represents distance above or below sea level The domain for this graph is best represented using a set of 1 Integers 3 Positive Integers

4 The solution to 3 x 8 4x 8x 4 is 1 12 2 28 3 12 4 28

2 Nicci s sister is 7 years less than twice Nicci s age a The sum of Nicci s age and her sister s age is 41 Which equation represents this relationship 1 a 7 2a 41 3 a 2a 7 41 2 2a 7 41 4 a 2a 7

Sketch a 45 45 90 triangle with a hypotenuse of 7 Label the other side lengths

3 a 2 C 4 2 2 4 6 8 10 1 3 Is the degree of the polynomial odd or even Explain how you know odd The degree is 3 b Is the sign of the leading term of the polynomial positive or negative X What is the constant term of the polynomial

Eliminate the parameter t Then use the rectangular equation to sketch the plane curve represented by the given parametric equations Use arrows to show the orientation of the curve corresponding to increasing values of t x 4 cost y 3 sint 0st 2t The rectangular equation is with

C 5b T2 The Lush Landscaping Company is involved in a project for the city They will be enlarging the garden in front of City Hall The current dimensions of the garden are 24 feet long by 16 feet wide The company plans to make the garden area larger by planting a border of white flowers all the way around the existing garden The border will have the same width x around the entire garden d Let x represent the width of the white flower border Complete the expressions for the length and the width of the new garden space after the border has been added in terms of x length 24 width 16 24 feet b Write an expression representing the rectangular area of the new garden space after the border has been added as a product of the length and width in terms of x 16 fee Using your expression from part b write a trinomial expression that represents the rectangular area of the new garden space after the border has been added Using your expression from part c write a polynomial expression that represents the area of the border of the landscape company plans to add

x 4 1 3x 6 7 from f x

Use algebraic methods to solve the following equations for a a 4 18 x 4 5 b 15 9 2 8 45 2 c 8 96 0 89 x 38 Preview DE Preview Preview

principal 12 000 interest rates 14 date repaid October 07 how many days and what the simple interest and amount paid back

The population of a town has been growing following the equation P 400t 4000 where t is years after 2010 The number of restaurants in the town has been growing according to the equation R 5t 35 Complete an equation for the number of restaurants per capita per person Restaurants per capita

Select all the points of intersection between the graphs of the functions f x x 5 x 2 and g x 2x 1 x 2 5 2 0 5 2 a 5 0 b 1 0 d 2 0 4 c 2 12 3 What are the solutions to the equation x 3 x 5 Rewrite the equation in standard form then factor and solve algebraically Draw a rough sketch of the graph of g x x x 2 Label key points end behavior Explain your work e 4 18 f 5 30 intersection 2 15

Unit 2 Lesson 2 Cumulative Practice Problems 3 1 Select all polynomial expressions that are equivalent to 6x 4x 7x 5x 8 Explain a 16x b 10 6x 4x 7x 5x 8x e 8 5x 7x 4x 6x d 8 5x 7x 4x 6x

rsh B s 207 15 10 D A C 10 86 4 2 YA 5 10 15 20 E F G 2 4 6 8 61 H Point A b Point B Point C a C d e f ind g Point D Point E Point F Point G h Point H 05 50 Hese of is wrong 1 bo aut ostumes ALORS blivion to and 70 eistiacering 15 2 Add one term to the polynomial expression 14x 9 9x 5 11x 5x 3 to make it into a 22nd degree polynomial

Unit 2 Lesson 5 Cumulative Practice Problems 3 1 Which polynomial function has zeros when x 2 x 1 or x 5 h a f x x 2 3x 4 x 5 b f x x 2 4x 3 x 5 f x x 2 3x 4 x 5 d f x x 2 4x 3 x 5 C

4 The graph given below models the Nemo s distance from home in miles after x hours of swimming Two coordinate points have been labeled 3 5 and 6 10 a Interpret the point 6 10 in the context of this situation in a complete sentence Distance from home b What would the units be for the average rate of change in this scenario Answer 3 5 Time 6 10 x

3 f x x 2 f g f g fg Domain x x 1 2x 1 8 x f g X 2 X 2x 1 x 1 x 2 x 1 x 2x 1 2x 1 x 1 x 2 X 2x 1 x 1 Domain x 1 x 1 Domain x 2 X 2x 1 x 1 x x 2 2x 1 x 1 2x 1 Domain x 2 x 1 x 2x 1 2x 1 x 1 2x 1 X X BIOG nimmod 2 b

If a person shoots a basketball overhand from a position 8 feet above the floor then the path of the basketball through the hoop can be 16x 1 15x 8 where v is the initial velocity of the ball in ft sec y is the height of the ball and x is the 0 434v modeled by the parabola y distance away from the person a If the basketball hoop is 10 ft high and located 20 ft away what initial velocity v should the basketball have b What is the maximum height of the basketball a The initial velocity of the basketball should be approximately ft per sec Round to the nearest hundredth

Suppose you have a function f x and all you know is that f 4 6 and the graph of its derivative is Click on the graph to see a bigger version Use linear approximation to estimate f 4 2 Is your answer a little too big or a little too small Enter TB or TS 1 0

What is the equation of the function shown in the graph given that the equation of the parent function is f x g x 2 g x 3 o g x 3 ar 4 FP ER y 4 g x 1 3 3 2 n E Ba 50 SPE h 0 3 2 3

Which graph represents f x 5 3 2 1 6 5 4 3 2 1 1 2 1 2 3 4 5 67 6 5 4 3 X

13 11 11

3 1 pt Suppose a bag contains equal numbers of red marbles and red cubes and twice as many blue marbles as red marbles You reach in with your eyes closed and take out one item Which of these best describes the probability of getting a blue marble likely unlikely or roughly even chance Justify your answer with an example or an explanation

The profit of a company in dollars is the difference between the company s revenue and cost The cost C x and revenue R x are functions for a particular company x represents the number of items produced and sold to distributors C x 2100 60x R x 860x a Determine the maximum profit of the company The maximum profit of the company is

Solve the following system y 1 2 x 6 x 5 y x 1 5 Show Your Work

11 6mn 3m n 8m n 5m n 5m n 6m n 5m n 6m n 3m n A 6m n 10m n 5m n 9m n 6m n 6mn B 6m n 10m n 5m n 9m n 5m n 6mn 4 C 6m n 11m n 5m n 9m n 6m n 6mn 4 D 6m n 11m n 5m n 9m n 2m n 6mn

Refer to the three images below to complete the problems that follow Check your answers using the link at the bottom of the page f x x 3 1 Find 3 Find the value for x when 2 For how many values of x does 4 Evaluate 5 Evaluate 6 Evaluate X 2 7 Is Explain 0 1 2 g x 5 52 2 1 2 25 32 h x

2 12 6u y 7v 2uv 4u v u v 8u 5u v 6v 4 3v 1 A 4u v 6v4 4v 2uv 8u B 4u v 5v4 4v 2uv 8u C 4u v 3v4 4v 2uv 8u D 4u v 5v4 4v 2uv 5u

9 1 2x y4 8x 8xy 5 4x y 6xy 8x4y x4 A 5x y 9x 10xy 4 B 2xy 9x 10xy 4 C 5x y 9x 10xy 10 D 2xy 9x 14xy 4

Simplify 1 8 6 40 2 18 3 24 7 45 8 54 12 72 13 68 14 4 27 9 49 15 2 5 32 10 56 16 11 44 17

Polynomial Addition Simplify each sum 1 3n 8n2n n A 5n4 8n C 7n 8n 3 3x 8 2x 8 A 2x C 4x B 7n D 7n 5n B 5x D 2x 6 5 4u8u y 3u v 2u A 5u y u4 B 8u y u C 5u y 2u4 D 5u v 7 8y 3x 2x 3y A x 4y C x 3y B x 11y D x 9y 2 4 6 8 2 2n6n 5n 3n A 6n 5n4 C 3n 2n 4 4p 8 7 3p A 4p 3p 1 B 2p 4p 1 C 2p 4p 4 D 2p 3p 1 6 4m n m 7m2m n A 7m n 8m B 16m n 8m C 6m n 8m D 8m n 8m 8 56 8 5 5b4 A 3 C 3 B 3n 3n D 5n 2n B 1 D 5

Polynomial Addition Simplify each sum 1 3n 8n2n n A 5n4 8n C 7n 8n 3 3x 8 2x 8 A 2x C 4x B 7n D 7n 5n B 5x D 2x 6 5 4u8u y 3u v 2u A 5u y u4 B 8u y u C 5u y 2u4 D 5u v 7 8y 3x 2x 3y A x 4y C x 3y B x 11y D x 9y 2 4 6 8 2 2n6n 5n 3n A 6n 5n4 C 3n 2n 4 4p 8 7 3p A 4p 3p 1 B 2p 4p 1 C 2p 4p 4 D 2p 3p 1 6 4m n m 7m2m n A 7m n 8m B 16m n 8m C 6m n 8m D 8m n 8m 8 56 8 5 5b4 A 3 C 3 B 3n 3n D 5n 2n B 1 D 5

Polynomial Addition Simplify each sum 1 3n 8n2n n A 5n4 8n C 7n 8n 3 3x 8 2x 8 A 2x C 4x B 7n D 7n 5n B 5x D 2x 6 5 4u8u y 3u v 2u A 5u y u4 B 8u y u C 5u y 2u4 D 5u v 7 8y 3x 2x 3y A x 4y C x 3y B x 11y D x 9y 2 4 6 8 2 2n6n 5n 3n A 6n 5n4 C 3n 2n 4 4p 8 7 3p A 4p 3p 1 B 2p 4p 1 C 2p 4p 4 D 2p 3p 1 6 4m n m 7m2m n A 7m n 8m B 16m n 8m C 6m n 8m D 8m n 8m 8 56 8 5 5b4 A 3 C 3 B 3n 3n D 5n 2n B 1 D 5

Write each expression in radical form 1 7 2 2 3 2 2 3 5 6 2 4 6

Polynomial Addition Simplify each sum 1 3n 8n2n n A 5n4 8n C 7n 8n 3 3x 8 2x 8 A 2x C 4x B 7n D 7n 5n B 5x D 2x 6 5 4u8u y 3u v 2u A 5u y u4 B 8u y u C 5u y 2u4 D 5u v 7 8y 3x 2x 3y A x 4y C x 3y B x 11y D x 9y 2 4 6 8 2 2n6n 5n 3n A 6n 5n4 C 3n 2n 4 4p 8 7 3p A 4p 3p 1 B 2p 4p 1 C 2p 4p 4 D 2p 3p 1 6 4m n m 7m2m n A 7m n 8m B 16m n 8m C 6m n 8m D 8m n 8m 8 56 8 5 5b4 A 3 C 3 B 3n 3n D 5n 2n B 1 D 5

Polynomial Addition Simplify each sum 1 3n 8n2n n A 5n4 8n C 7n 8n 3 3x 8 2x 8 A 2x C 4x B 7n D 7n 5n B 5x D 2x 6 5 4u8u y 3u v 2u A 5u y u4 B 8u y u C 5u y 2u4 D 5u v 7 8y 3x 2x 3y A x 4y C x 3y B x 11y D x 9y 2 4 6 8 2 2n6n 5n 3n A 6n 5n4 C 3n 2n 4 4p 8 7 3p A 4p 3p 1 B 2p 4p 1 C 2p 4p 4 D 2p 3p 1 6 4m n m 7m2m n A 7m n 8m B 16m n 8m C 6m n 8m D 8m n 8m 8 56 8 5 5b4 A 3 C 3 B 3n 3n D 5n 2n B 1 D 5

Polynomial Addition Simplify each sum 1 3n 8n2n n A 5n4 8n C 7n 8n 3 3x 8 2x 8 A 2x C 4x B 7n D 7n 5n B 5x D 2x 6 5 4u8u y 3u v 2u A 5u y u4 B 8u y u C 5u y 2u4 D 5u v 7 8y 3x 2x 3y A x 4y C x 3y B x 11y D x 9y 2 4 6 8 2 2n6n 5n 3n A 6n 5n4 C 3n 2n 4 4p 8 7 3p A 4p 3p 1 B 2p 4p 1 C 2p 4p 4 D 2p 3p 1 6 4m n m 7m2m n A 7m n 8m B 16m n 8m C 6m n 8m D 8m n 8m 8 56 8 5 5b4 A 3 C 3 B 3n 3n D 5n 2n B 1 D 5

Simplify 1 25 92 27 10000006 29 49 2 1 31 64n 2 26 343 3 AIDA 28 36 30 9 1 32 81m

Match each of the following graphs with the correct function by placing the letter of the graph on the line provided Each letter can only be used once Do not use a calculator or desmos to draw the grap J H 3 100 2 1 X 2 F 12 1 1 1 1 0 a 1a E 41 2 1 B 5 10 272x 1 q 1 x 1 x 1 2 C 1 G 6 f x x 2 fi x x 1 7 f x x 3x 2 9 1 b 1 CHO 9 1 a l 1 2 x 3 1 100 201 2 0 c 2 8 f x x 2x 10 D 9 f x 2 2 x 1 1 1 2 1 3 X 1 F 0 1 1 2 1 1 2 1 10 f x x 2x x 1 x 2 To H 1 1