Quadratic equations Questions and Answers

20 Given p x 4x 1 and q x x 3 find each pop x qq 2

2 Write the equation of the line shown on the graph in slope intercept form 3 5 4 3 2 19 1 2 3 4 5 9123 3 4 45 5 Type a response X

8 Which table of values does NOT represent a direct variation X y X y X y X y 2 10 1 10 1 5 2 1 2 20 0 1 0 3 1 2 0 0 26 2 1 3 4 30 1 2 15 5 40 39 2 1

3 Write the equation of the line shown on the graph in slope intercept form 5 4 3 2 1 5 4 3 2 1 2 5 4 5

There were 24 1000 students that were prefects What was the percentage who were given that responsibility

Graph the solution set of the following linear inequality Answer The line will be drawn once all required data is provided and will update whenever a value is updated The regions will be added once the line is drawn Enable Zoom Pan Choose the type of boundary line Solid a Dashed 4x 15 4y 15 Enter two points on the boundary line 8A

Graph the circle after writing the equation in standard form x 2x y 10 10y 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 1 73 1 2 3 4 6

Solve the system of equations y x 2 y x 1 3

What is the solution for in the equation 36 25x 0 36 A 25 B O C OD x 9 25 36 10

ph the circle by rewriting the equation in standard form x y 4x 4y 1 0 6 5 T 3 2 1 Ty 6 85 4 3 N 1 2 5 1 2 3 4 5 X

10 216x 6x 10 3x 6 h 6x 1 3x x 10 37 11 64 x 4 165x 4 3 2x 4 2 5 3 2x 4 2 5x 6x 12 10x 6 6x

10 WI IN 2 12 3 13 4EEE 14 5 1 a 15 16 D 17 H 8 18 9 19

1 Examine the graph of f x at the right and identify the following significant features Is the graph a function How can you tell b y intercept s c x intercept s d f 3 what is the output when x 3 Estimate the value it will be a decimal Find value s of x when f x 2 AN

Solve the following system of linear equations by substitution and determine whether the system has one solution no solution or an infinite number of solutions If the system has one solution find the solution Answer Keypad Keyboard Shortcuts Selecting an option will enable input for any required text boxes If the selected option does not have any associated text boxes then no further input is required One Solution Correct O No Solution 4x y 8 8x 2y 10 Infinite Number of Solutions

Solve the following system of linear equations by addition Indicate whether the given system of linear equations has one solution has no solution or has an infinite number of solutions If the system has one solution find the solution Answer Keypad Keyboard Shortcut Selecting an option will enable input for any required text boxes If the selected option does not have any associated text boxes then no further input is required One Solution 8x 2y 30 2x 2y 6 No Solution Infinite Number of Solutions

Describe the sequence of transformations from the related common function f x x to g g x x 9 O reflection in the x axis then vertical shift 9 units down reflection in the x axis then vertical shift 9 units up O reflection in the y axis then vertical shift 9 units up O reflection in the y axis then horizontal shift 9 units right O reflection in the y axis then horizontal shift 9 units left

answer Add State the sum in simplest form 6 3 7x 2y 9 O 14xy 42x 6y 14xy 9 O 7x 2y may be uneven because questions can be worth more or less including zero depending on ye 12y 21x 14xy

tion 3 of 7 Step 1 of 1 Find the equation for the line that passes through the point 5 2 and that is perpendicular to the line with the equation x 4 10 Correct 10 Enable Zoom Pan 5 A

Consider the following y intercept and slope 0 2 m 1 Step 2 of 2 Determine the graph of the line with the given y intercept and slope Answer The point given for the y intercept 0 2 is marked on the graph Points can be moved by dragging or using the arrow keys Any lines or curves will be drawn once all required points are plotted and will moved Enable Zoom Pan

Find the domain of the rational expression O all real numbers except 3 O all real numbers except 8 O all real numbers except 21 all real numbers except 0 8 x 7x 2

6 12 Correct 0 Incorrect The given table shows the urban growth of New York NY by providing the estimated population from 1850 to 2000 The population for each year is shown in thousands Year 1850 1900 1950 2000 Answer How to enter your answer opens in new window Population in thousands 500 4000 8500 9000 Step 2 of 2 Find the slope of the line segment that represents the change in population in thousands from the year 1900 to 1950 Keypad Keyboard Shortcuts Previous Stan Answer

New Vocabulary Steep Steep Steep is another word for slope The greater the slope A m 2 Line 34 is steeper than Line B m 3 0

A m Line you 0 is steeper than Line B m N 7 0

10 10 10 Domain XE 0 5 U 5 00 Range ye Intervals of Increase Intervals of Decrease Maximum Minimum 10 4 2 1 0 1 2 3 4 Domain Range Intervals of Increase Intervals of Decrease Maximum Minimum 1 2 3 4

After begging her parents for 3 years Sophia is finally going to clown college On the first day her juggling instructor divides a box of bean bags equally among the 17 clowns in Sophia s class Each clown gets 4 bean bags Which equation can you use to find the number of bean bags b in the instructor s box b 17 4 17b 4 b 17 4 b 17 4 Solve this equation for b to find the number of bean bags in the instructor s box bean bags

1 point Ron needs to cut out a felt shape for his art project The diagram below provides the dimensions of the shape 5 cm 25 cm 11 cm 9 cm Enter your answer in the box 3 cm 17 cm How much felt is in the shape for the art project

g is related to one of the parent functions described in this chapter a Identify the parent function f b describe the sequence of transformations from fto g c Sketch the graph of g 8 g x 2 x 5 7 g x x 4 3

2 Identify the parent function and write an equation for each function whose graph is shown a c y 2 b d K 8 12

Objective In this lesson you will learn how to identify and graph various functions a Write a linear function f such that it has the indicated function values and b sketch the graph of the functio 1 f 3 8 f 1 2

olve for the roots in simplest form using the quadratic mula 4x 3 12x 29 Solve for the roots in simplest form using the quadratic formula 2 16x 100 31 What are the roots of the equation x 8x 25 0 in simplest a bi form 32 What are the roots of the equation x 8x 17 0 in simplest a bi form

Relationship A has a greater rate than Relationship B This table represents Relationship B Hours worked Amount paid 2 y 11 5x y 13x y 12 75x y 12 25x 25 Which equation could represent Relationship A Hours worked is represented by x and amount paid is represented by y Select each correct answer 4 50 5 62 50 8 co 100

A company produces very unusual CD s for which the variable cost is 13 per CD and the fixed costs are 20000 They will sell the CD s for 89 each Let a be the number of CD s produced Write the total cost C as a function of the number of CD s produced C Write the total revenue R as a function of the number of CD s produced R Write the total profit P as a function of the number of CD s produced P Find the number of CD s which must be produced to break even The number of CD s which must be produced to break even is

Question 4 7 6 5 A Slope m US 3 2 1 7 6 5 4 3 2 1 1 7 2 3 4 5 6 7 Find the slope of the line 1 2 3 4 5 6 7 a E Enter your answer as an integer or as a reduced fraction in the form A B

6 5 4 3 2 9 5 4 3 2 1 2 2 3 4 6 AUT 2 3 4 5 6 The graph above is a transformation of the function f x x Write an equation for the function graphed above g x

Solve the equation 6 2 2x 1 8 The solutions are

Solve the equation 5x 3 11 The solutions are

If you forget here are the steps 1 How many times does the denominator go into the numerator that becomes whole number 2 What is leftover that becomes the numerator 3 Denominator stays the same 1 4 23 6 42 9 2 5 54 10 51 10 3 6 7 2 63 8 11

5 60 n 5 12 5 12 5 12 2053 2011 21 14157 2012 02 26 6 36x 11 11 2012 32x 23 3 10 2 2 100 30 2 6 10 27 3 200 30 24 60x 0 3a 28a36 2 72 2 9 28 2 72 2 36 2 18 2 9 29 2

Write BC in component form with B 0 8 and C 1 4 BC

The graph of f z is shown in red Draw the graph of g x f z 1 Make sure to start at one of the endpoints not the middle point After finishing the graph click outside the grid to stop drawing The graph of f x is shown in red Draw the graph of g x f x Make sure to start at one of the endpoints not the middle point After finishing the graph click outside the grid to stop drawing 8 6 5 4 3 2 1 3 4 5 6 7 Clear All Draw Polygon 8 7 6 5 8 7 6 5 4 3 2 1 12 4 5 6 Clear All Draw Polygon 436

Given functions f x interval notation f x m 1 Domain of f m x Domain of Domain of m f x video 1 and m x x 4 state the domains of the following functions using T

I I 5 g f x and g Let f x Find the following functions Simplify your answers f g x 7 I

Function Composition Using Graphs Use the graphs for f x and g x to evaluate the expressions below Write your answer as an integer or a reduced fraction 6 5 4 6 5 f g 5 g f 2 f f 3 g g 1 3 2 1 J1 f x 5 6 6 4 3 2 6 4 3 2 3 4 5 6 12 3 X 6

3 2 1 5 4 3 2 1 3 1 2 3 4 Lur The function graphed above is Increasing on the interval s Decreasing on the interval s

A Use the graph of f x to evaluate the following 6 5 4 3 2 7 e The average rate of change of f from x 0 to x 2 is Give your answer as an integer or reduced fraction 3 4 5 X 6

Sketch a graph of f x 5 4 3 2 2 5 Clear All Draw 4 3 2 Fond 1 if 2 1 if 3 if 2 1 2 3 4 1 1 1 1 unt 1 2 3 4 5 11 Note Be sure to include closed or open dots but only at breaks in the graph

Match each graph with its equation y T vy x y x 1 x 1 AC y y x y y AANME Vx x 3 a b 5 4 3 2 2 2 5 5 4 3 2 1 5 54 3 2 2 1 3 4 5 a w

Consider the following quadratic equation x 2x 12 Determine the constant that should be added to both sides of the equation so that the left side becomes a perfect square trinomial is the required constant Solve the quadratic equation by completing the square Enter solutions using a comma separated list T X

Question 12 Solve the following quadratic type equation Enter solutions using a comma separated list x 14x 49 0

In Exercises 23 28 evaluate the expression 23 323 5 8 24 12523 25 25 36 2 36 26 243 25 g 27 128 128 28 34343 2401