Quadratic equations Questions and Answers

What are the solutions for the given equations below 3n 27 O

Select Yes or No to indicate whether each ordered pair is a point of intersection between the line y x 1 and the parabola y x 1 Ordered Pair 0 1 1 2 2 0 Yes No 0 0

Solve the system of equations x 2 y 2 x

A The system of equations below is represented by which of the following graphs P y 3 x 1 y 2x 5 C 19 dn 44 Y o d B D 39 40 17 T 24 24 44 7 9 5

2 y 4x 6y 4 0 6 5 4 3 2 1 5 4 3 2 1 0 T 2 3 2 N 3 4 5 to 6

2 Find the exact value of the following logarithmic expression logs

The complex number 9 6i represents which radical expression below A 9 36 B 9 36 C 9 36 D 9 36

7 At a local garden shop the price of plants includes sales tax The cost of 4 large plants and 8 medium plants is 40 The cost of 5 large plants and 2 medium plants is 28 a Ifl is the cost of a large plant and m is the cost of a medium plant write a system of equations that models this situation b Could the cost of one large plant be 5 50 and the cost of one medium plant be 2 25 Justify

3 The graph of a quartic function f is shown on the ry coordinate plane Write an equation for f 2 A 12 8 0 4 8 1 2 16

4 If the function f x 1 0 1 2 3 3 0 1 1 2 x has the domain 0 1 4 9 what is its range 2 0 1 16 81 4 0 1 1 2 2 3 3 16 16 81 813

6 Solve algebraically for y 4 y 3 4 2y 1

2 A function is defined as K x 1 54 2 0 2x P 1 5x 3 The value of K 3 is 4 3 36 18

5 Is the product of 16 and rational or irrational Explain your reasoning

L Given 7x 2 58 which number is not in the solution set 1 6 2 8 4 12 3 10

7 Decide if each set of conditions is possible If so give an example If not explain why not a A 5th degree polynomial with no turning points b A 3rd degree polynomial with three turning points c A 4th degree polynomial with two turning points

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

5 The graphs of a function and its derivatives y f x y f x and y f x are shown Determine which graph is which f x f x f x Let A represent graph with thin solid line Let B represent graph with thick solid line Let C represent graph with dotted line

1 For F ax by find F dr across the first quadrant of the circle with radius 2 centered at the origin and oriented counterclockwise 8 points

Let g x 2 3x 4 x 1 x 3 be a polynomial function Name all horizontal and vertical intercepts of the graph

D 790426ab090 2 simplify 6a 5a 8 2 4a 6a O O 2a 14a 4 2a 11a 4 O 2a 14a 1 2a 11a 10 3 Simplify 6n 4n 3 8n 6n 1 12n 4 O

3 Which value for x below is a solution to the equation 2x 8x 20 5x a 1 b 2 p 4 d 5

The pH of a chemical solution is given by the formula pH log 0 H where H is the concentration of hydrogen ions in moles per liter Values of p 10 range from 0 acidic to 14 alkaline Answer parts a through f po ype all meyer un autcimal d What happens to pH as the hydrogen ion concentration decreases pH decreases O pH increases e Determine the hydrogen ion concentration of a solution with pH 3 2 H M Round to six decimal places as needed f Determine the hydrogen ion concentration of a solution with pH 7 8 COB

5 poir After 3 days a sample of radon 222 decayed to 58 of its original amount What is t half life of radon 222 to 2 decimal place

The pH of a chemical solution is given by the formula pH log 10 H where H is the concentration of hydrogen ions in moles per liter Values of pH range from 0 acidic to 14 alkaline Answer parts a through f a What is the pH of a solution for which H is 0 001 pH Type an integer or a decimal b What is the pH of a solution for which H is 0 0001 pH Type an integer or a decimal c What is the pH of a solution for which H is 0 00001 pH Type an integer or a decimal d What happens to pH as the hydrogen ion concentration decreases

2 Identify the value for x that is not a solution to the inequality 4 4x 8 a 0 b 2 c 3 d 10

4 Simplify 4x 8x 3x 6x O O 21x 0 7x 14x 12x 14x 12x 17x 4x 14x

3 Simplify 6n 4n 3 8n 6n 1 O O 12n 4 17n 4 11n 17n 4 4n 17n 4 4 Simplify

Questions 8 9 10 11 12 Find the area of the shaded region 2x 3 2 simplify 3x 2 4x 5 6a 5a 8 2a 14a 4 x 8 zoom in 2 4a 6a 1 Write an expression that represents the area that is shaded Type a response

Consider the following f x 1 X 4 a State the domain of the function all real numbers x except x 4 O all real numbers x O all real numbers x except x 4 O all real numbers x except x 4 and x 4 all real numbers x except x 1

Find the exact value of the logarithm without using a calculator In 2 e 12

Fill in the blank with an inequality symbol for the following statements that can be satisfied by the value x 2 3x 4 2x 2 3x 4 2x 4 2x 4 4x 3 x 4 12 10 2x 5 5x 10 4x5 2x 24 x 1

Quickwrite Is x 4 a solution to the equation and the inequality shown below 3x 2 10 3x 2 10 a equation only b inequality only c both the equation and the inequality d neither the equation nor the inequality Explain

9 Which value of x below is a solution to the inequality 3x 2x 8 0 a 3 b 2 c 1 d 0

8 Which value for t below is a a solution to the given inequality 2x 4 3x 5 a 10 b 6 c 2 d 10 e 15

7 Which value for q below is a solution to the inequality 3 q 4 2q 10 a 30 b 20 c 10 d 0

6 Give 5 possible solutions to the inequality 3x 10 21

4 Choose all possible values for x below that satisfy the inequality 4x 10 20 a 20 b 8 C 7 d 2 e 10

5 Which value below is a solution to the inequality 3x 2 2x 4 Select all that apply a x 2 b x 0 c x 5 d x 7

2 Which values for x below are solutions to the inequality 5 x 2 a 10 b 20 c 2 2 d 6 e 9

Independent Practice 1 Which values for x below are solutions to the inequality 3x 12 Select all possible solutions showing your work clearly a 10 b 5 c 0 d 5 e 10

3 Which solutions below are a solution to the inequality shown 2x 4x 4x 8 a x 2 b x 4 C X 0 d x 2

Partner Practice 1 Identify all values for x below that are a solution to the inequality 2x 4 10 a 2 b 1 c 3 d 5 e 10

Find the exact value of the logarithm without using a calculator in Ve

Find the exact value of the logarithm without using a calculator log 381

Find the exact value of the logarithm without using a calculator log 12144

The owners of a circus are planning a new act They want to have a trapeze artist catch another acrobat in mid air as the second performer comes into the main tent on a zip line If the path of the trapeze can be modeled by the parabola y x 16 and the path of the zip line can be modeled by y 2x 12 at what point can the trapeze artist grab the second acrobat Above are two trapeze artists catching each other in midair In this new act a person on a zipline will glide right through which for timing essential

Graph the circle by rewriting the equation in standard form x y 4x 4y 1 0 1 Ty 6 65 5 4 3 2 1 N 3 4 5 1 2 3 4 10 8

x y 7 x y 7 2

linear quadratic system algebraically Solve the given y x 2x 4 y 2x 4

Ty 5 6 5 4 3 2 1 000 3 2 1 1 2 3 4 2 3 4 5 7 Which of the following points is on the circle centered at 8 9 with a radius of 10 unit A 0 3 B 3 5 C 9 1