Quadratic equations Questions and Answers

5 Determine which sets are bases for R2 or R Justify each answer 5 CHE 4 a L T P L 7 3 L5 J J L 2 FOT

1 2 3 4 lim f x X4 2 lim f x lim f x 5 lim f x 6 lim f x 7 lim lim f x 8 lim f x of f x above evaluate the limits below 9 lim f x x 1 2 1 H

8 6 ARE Y 8 6 4 2 4 8 V 2015 y g x 68 y f x CADASINDA sex

9 77 B 18 7 6 5 4 3 2 2 1 0 1 2 3 4 5 1 1

A small radio transmitter broadcasts in a 41 mile radius If you drive along a straight line from a city 56 miles north of the transmitter to a second city 55 miles east of the transmitter during how much of the drive will you pick up a signal from the transmitter miles

Problem 6 3 In R4 compute the matrix in the standard basis of an orthogonal projection on the two dimensional subspace spanned by vectors 1 1 1 1 and 2 0 1 1

x 6 y 1 37 7 x 12x 36 y 2y 1 37 36 1 37 x y x 2y 0 r 125 os 0 2rsin 0 0 r r r r r 12 cos 0 2 sin 0 0 r 12c050 2 sin O 3 formulas p x y

Factor the following JQUE DOCuer holour 4y 24y 36y

6 Solve for x x 12 3x 7 Solve for x 4x 6 10

3 Find the equation of the line perpendicular to 8x 6y 54 0 and passes through point 32 5 4 Two thirds of the sum of a number and 14 equal 3 times the number find the number

Write an equation for the function graphed below 15 2 ATM 17 7345 31 Mar M O

Use the graph below to determine the value of f g 4 Do not include f g 4 in your answer 7 6 5 4 2 1 3 2 1 0 1 0 1 2 3 4 5 6 g x f x 7 8 9 10

Expand and simplify 4x 3y 3y 4x 3y

The graph of f x x 1 x 5x 6 is shown Select the zero s of f www Ay 6 4 2 no zeros 5 0 10 10 20 30 40 1 9 4 4 8 3 2 X 7 2 3 6 1 4

3x 2 4 x 2 Sx 10 and write the answer in simple

17 16 1514 13 12 11 10 9 7 6 54 3 2 4 3 2 24 3 1 2 3 4 5 7 8 10 11 The curve above is the graph of a sinusoidal function It goes through the points 11 4 anc 3 4 Find a sinusoidal function that matches the given graph If needed you can enter 3 1416 as pi in your answer otherwise use at least 3 decimal digits f x

2 Factor completely b 8x 8x 48

Function Composition Use the table of values to evaluate the expressions below f x g x 1 1 5 3 C 5 4 3 2 1 O 1 2 3 45 2 52 0 4 34 0 1 5 53 3 2 4 2 35 1 f g 5 g f 2 f f 3 g g 1

Describe the key features of the Function f x 5 AX intercept 0 intercept 1 Horizontal asymptote at the x axis B X intercept None Y intercept A Horizontal asymptote at the X axis 0 X intercept None Y intercept 5 Horizontal asymptote at the x axis D X intercept 5 y intercept None Vertical asymptote at the 4 axis

The system of linear equations O has infinitely many solutions O has 0 solutions O has exactly 2 solutions O has exactly 1 solution x 8y Y 3z 2z N 3 4 5

Lily and Maya have been driving for 3 34 hours They are 75 of the way to tpe their destination At this rate how many hours long is their total trip

Expand and simplify 4x 3y 8x x 3y

asymptotes horizontal asymptotes and holes Notes 5 4 5 5 Show complete work on your worksheet f x x 9 JA x Reduced function fred x Hole s x 12 Domain Select an answer by hand As sketching aids check for intercepts vertica O There is are vertical asymptote s at O There are no vertical asymptotes There is a hole at There is no hole in this function

4 In the figure below O is the center of the circle ZEAD B 40 and ED 40 Find ZDAB

Exponential Functions Question 8 What function is represented in the graph Select one Oy 4 25 Oy 4 3 Oy 3 4 Oy 2 25 10

4 What are the approximate coordinates of the point of intersection of the two graphs What does this mean in terms of the two mold populations area square millimeters 900 800 700 600 500 400 300 200 100 B A

The graph of y f x is shown below What are all of the real solutions of f x o 10 8 6 4 2 10 8 6 4 2 2 4 6 8 y 10 2 4 6 10

f x is graphed below What is the average rate of change of the function f x on the interval 8 x 6 The function y y 20 18 16 14 12 10 8 6 4 10 9 8 7 6 5 4 3 2 1 2 4 6 8 10 12 14 16 18 20 2 3 4 5 6 7 8 9 10

and the equation of the exponential function represented by the table belov X 0 1 2 Y 4 12 36

Solve the equation 5 4x 2 2 10 2

Find the measure of the arc or angles Point P is the center of the circle R G P 84 66 S Q AGSR ARST mRT m ST II ARPT

f x x 5 x 0 a Find the inverse function of f 7 x c Describe the relationship between the graphs of f and 1 O The graph of f 1 is the reflection of f in the y axis O The graph of f 1 is the same as the graph of f The graph of f 1 is the reflection of f in the line y x O The graph of f 1 is the reflection off in the line y x The graph of f 1 is the reflection of f in the x axis d State the domain and range of f Enter your answers using interval notati domain range State the domain and range of 1 Enter your answers using interval notatic domain

Identify characteristics of the quadratic function and its graph 1 2 DAY 8 4 2 4 X 5 2 2 y AX

Question 9 Compute the difference quotient a f x 4 6x b f x 6x 7x 1 f x h f x h h 0

Question 23 Perform the operation and simplify the rational expression a b 12 4 2 28 4x 4x x 6 Y 19x 15x 25 2x 5 4x 9x 2 x 2x 8

Combine each of the following using addition Simply you result whenever possible 3 5 7x 14x a 3x 1 6 2x 5 9 X 1 b 10 15x c

Verse of the function shown below 8 7 6 5 4 3 a 1 8 7 6 5 3 2 1 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

13 y 2x 8x 3 14 y 2x 4x 1 15 y 5x 10x

Write the equation of the trigonometric graph 27 JAAA 2 2 help 2 4 3 2 1 1 2 y 3 4 2 2 3 2 2 5 x

3 Students will work independently and interdependently while striving for accuracy the following graph of a polynomial a peer came up with the equation p x x 1 x 3 x 2 but the end behavior doesn t match the graph of the function below Find the error s in your peer s work explain to them in words how they would correct it 4 5 4 3 5 3 0 2 5 2 1 5 1 0 1 0 5 2 0 0 6 6 10 12 0 5 14 1 1 5 2 0 25 3 3 5 4 45

8 Hanzo is paid semimonthly His semimonthly salary is 1 730 What is his annual salary A 41 520 B 44 980 C 20 760 D 34 600

The graph below shows the value of Bob s Beanie Baby collection over several years 3000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 1 2 The collection s value decreased at a rate of O dollars per Beanie Baby O dollars per year O Beanie Babies per dollar 3 4

14 What is the area of the circle 14 8 14 7x8 32

Reading a Graph Consider the graph shown below Profit in dollars 200 150 100 50 50 20 40 60 80 100 120 140 Interpret the meaning of the ordered pair 60 50 in this situation The profit will be Number of Candles Sold The profit will be dollars if are sold Interpret the meaning of the Vertical Intercept in this situation The profit will be dollars if candles are sold Interpret the meaning of the Horizontal Intercept in this situation dollars if are sold candles candles

The graphs of y f x the top function and y g x the bottom function are given below Use the line segment tool to draw the graph of y f x g x Make sure you pay attention to the domain of f x g x Provide your answer below Move Segment Undo Redo x Reset

The height y in feet of a ball thrown by a child is 1 x 2x 3 y 12 where x is the horizontal distance in feet from the point at which the ball is thrown a How high is the ball when it leaves the child s hand b What is the maximum height of the ball c How far from the child does the ball strike the ground Round your answers to the nearest 0 01 feet 6H You are working with a quadratic equation and construct the following graph 5 4 3 2 8 7 6 5 4 3 2 1 2 3 4 5 23 4 Identify the vertex of the parabola Remember that the vertex is a point 6 7 8 Identify the y intercept of the parabola Remember that the y intercept is a point feet and feet Identify the x intercepts Remember that the x intercepts represent points on the graph Write an equation for the axis of symmetry Given the x intercepts above write an equation for the parabola in factored form y Hint Think about the zero product property

Vertex y x 1 x 10 1 17 Formur y x 4x 15 TOLD y x 185 I

Advertising MI Budgeting Lesson 76 voice over work All changes s 1 Pauly created a budget for a new radio commercial After reviewing the budget however Jay realized Pauly included a extra field Which of the following was incorrectly included in the budget scriptwriter hair and makeup sound techs Dodson

Dilate the figure by the scale factor Then enter the new coordinates K 7 A 3 2 C 1 1 4 2 B A B C

Add the following polynomials Simplify your answer 3 3x x x 4x 5