Quadratic equations Questions and Answers

Determine the location of all critical points and determine their nature that is min max neither x 5x 12x 2x 3 Critical points ordered from smallest to largest X is a min max neither is a min max neither X Answer for blank 1 6 Answer for blank 2 1 Answer for blank 3 max Answer for blank 4 min

Solve the exponential equation 320 algebraically using logarithms Show your work and round your answer to three decimal places

A tunnel under a river is 196 8 ft below the surface at its lowest point as shown in the drawing If the angle of depression of the tunnel is 5 952 then how far apart on the surface are the entrances to the tunnel How long is the tunnel The entrances to the tunnel are ft apart on the surface Round to the nearest integer as needed The tunnel is ft long Round to the nearest integer as needed 15 9520 d 196 8 ft 5 952

Prove that the following equation is an identity 1 1 cos 0 csc 0 cot0 sin 0 Simplify the left side of the given equation csc 0 cot0 csc 0 cot 0

The vertical stretch by 2 then the vertical shift up by 3 The vertical shift up by 3 then the vertical stretch by 2 Reflect Are the resulting graphs the same Does the order in which we apply the graph transformations matter This phenomenon is sometimes called the Socks then shoes vs Shoes then socks problem In this last step we are going to go back to our first reflection We asked the question Are vertical stretches shrinks and horizontal stretches shrinks basically the same thing Yes that s right we re asking the first question again This time apply the following sequence of transformations to your chosen function f x Graph Transformations f x x2 The vertical stretch by 4 then a vertical shift by 2 A horizontal shrink by 2 and then a vertical shift by 2 A vertical shift by 2 then a vertical stretch by 4 A vertical shift by 2 then a horizontal shrink by 2 Reflect Compare and contrast the results of all transformation sequences Are there any changes to

rices and row reduction by hand to find the general flow pattern of the following network What is the minimum and maximum values of x 200B 300 x5 X X3 100 X X 200 X6

What is the function f x represented in the following table A B XOH23 0 1 f x 10 4 2 4 4 10 20 45 10 8 6 g x to 80 P 2 N 4 0 4 810

Suppose a projectile is launched from a tower into the air with an initial velocity of 48 feet per second Its height h in feet above the ground is modeled by the following function h t 16t vot 64 where t is the time in seconds since the projectile was launched and Vo is the initial velocity What domain makes sense for the function in this context 00 t 2 All positive numbers 00 t 4 All real numbers

10 3 0 5 10 5 0 5 10 0 15 20 5 0 1 16 Og x x 3 x 5 Og x x 3 x 5 Og x x 3 x 5 a x 3 x 5 10

Given the graph of the function y f x below draw the graph of y 2 f x Provide your answer below Move Parabola 10 9 8 7 6 5 4 3 2 T 2 TU 9 8 7 6 5 4 3 2 1 Undo 1 2 3 4 Redo 10 5 6 0 7 x Reset 8 9

ind the zeros and intercept Examide 2 g x x 3 x lost on 4 to solve

What is the solution of the quadratic equation 2x 5x 1 0 Solve by using the quadratic formula 5 17 4 O 5 33 4 5 33 4 O 5 17 4

Let T R R be the linear operator defined by T x y 8x 5y 3x 2y Then T x y HINT Recall T T x y x

8 If Csc 8 O cotA O cote O cote which equation represents cote 16 8 15 7 L 7 15 15 H GE

If cos es 0 3090 which of the following represents approximate values of sine and tan e for 0 e 90 O sin es 0 9511 tan es 0 3249 Osin es 0 9511 tan es 3 0780 sin 9s 3 2362 tan s 0 0955 sin 93 2362 tan es 10 4731

7 5 4 3 2 1 L f 21 X Of x 6 cos x Of x 3 cos x 3 Of x 6 sin x Of x 3 sin x 3

The blades of a windmill turn on an axis that is 30 feet from the ground The blades are 10 feet long and complete 2 rotations every minute Write a sine model y asin bt k for the height in feet of the end of one blade as a function of time t in seconds Assume the blade is pointing to the right when f 0 and that the windmill turns counterclockwise at a constant rate O y 30 sin 50 10 O y 30 sin 30 Oy 10sin 10 Oy 10sin f 30

Which of the following are in the correct order from least to greatest 27 6 80 4 38 777 38 80 4 6 2 38 4 80 27 6 2 38 80 4 N

45 degrees O 5 3 10 3 5 3 10 5 X 30 degrees

Which function will have a y intercept at 1 and an amplitude of 2 O f x sin x 1 Of x 2 sin x 1 Of x cos x Of x 2 cos x 1

A weight attached to a spring is at its lowest point 9 inches below equilibrium at time t 0 seconds When the weight released it oscillates and returns to its original position at t 3 seconds Which of the following equations models the distance d of the weight from its equilibrium after t seconds 3 O d 9cos Od 9cos 5 d 3cos d 3cos 25

13 The Foster family just hired a landscaping company to put in a flower garden in their backyard They would like to have a walkway around the garden The picture below represents the flower garden and the surrounding walkway 12 points total 2x 10 Walkway x 5 Flower Garden 2x 7 x 3 Write an expression in simplest form that represents the perimeter of the structure 2 x 3 2 2x 10 Write an expression in simplest form that represents the area of the entire structure Write an expression in simplest form that represents the area of the garden Write an expression in simplest form that represents the

10 8 6 4 2 10 8 6 2 2 4 6 8 91 6 18 8 10

For y 0 x A 1 B 4 C y D 14 E yo OA OB C OD ST 2 J is equivalent to

Solve the inequality and write your answer using interval notation 5 Points x x 1 2 x 2 The solution set is 2 1 U 3 0 The solution set is 2 2 U 3 2 The solution set is 2 2 2 2 The solution set is 2 2 U 2 2 I don t know

In the addition problem below the numbers being added have unknown digits signified by the letters A and B Assume that the unknown digits named by the same letter are the same digit Determine which of the following choices best describes the relationship of missing digits 5 Points 1ABA 32B 2205 A B 2 B A 1 A B 15 I don t know A B

12 10 pts Use the Cauchy Schwarz inequality to prove that 2 r 2 cos rdr 2

Suppose the functions f and g are defined by y f x 2 4 and y g x 2 respectively 2 2 1 Explain the steps of the transformation process that you would apply to the graph of g to obtain the graph of f 2 2 Write down the sets that represent the domain and the range of the function f and the equation of the asymptote of the graph of f 2 3 Sketch the graph of f including the asymptote represented by a broken line Label the horizontal and vertical axes and the x and y intercepts if any exist Determine the equation that defines the inverse function f 2 4 2 5 Show that fof x x and f of x x 3 4 6

87 95 models the horizontal distance d in inches of the pendulum of a grandfather clock from The equation d 11cos the center as it swings from right to left and left to right as a function of time t in seconds According to the model ho long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again Assume that right of center is a positive distance and left of center is a negative distance O 0 625 seconds O 0 8 seconds O1 25 seconds 1 6 seconds

Select one 19 O y 3 2 Oy 2 3 is represented in the graph 1 Oy 2 5 1 Oy 3 5 10 5 0 5 1

x in 8 in 7 in The function V x representing the volume of the box is listed below V x 4x 30x 56x Use the volume equation and your graphing calculator to find the values of x that result in a box with a volume of 15 cubic inches Identify all correct solutions

22 The following expression can be written as which algebraic expression in x 5 Points cos cot x 1 x x 1 x X 1 x None of these expressions

VERTICAL LINE TEST IF ANY VERTICAL LINE INTERSECTS THE GRAPH OF A RELATION A MORE THAN ONE POINT THEN THE RELATION IS NOT A FUNCTION NAME THE DOMAIN AND RANGE AND DETERMINE IF THE GRAPH IS A FUNCTION 54 24 1 1 1 1 3 2 1 2 4 0 0 1 2 3 x

NAME THE SLOPE AND Y INTERCEPT OF EACH LINE name the y intercept as an ordered pair AND THEN GRAPH THE LINE y 2x 5 6 3 f x x 4

21 Find all real solutions to the system of equations 5 Points xy 24 2x y 4 0 The solution set is 4 6 4 6 The solution set is 4 6 4 6 3 2 4 2 3 2 4 2 The solution set is 3 2 4 2 3 2 4 2 The system has no solutions I don t know

IF THE EQUATION IS NOT IN SLOPE INTERCEPT FORM THEN PUT IT IN THAT FORM BY SOLVING FOR Y THEN NAME THE SLOPE AND Y INTERCEPT GRAPH THE LINE 3x y 4 2x 5y 10 MAT 1033 view for Test 1 1

m is the slope and b is the y intercept y 2x 1 slope y intercept

Evaluate the following expression 5 Point 4 1 OO O 21 4 15 01 100 4 15 2 01 I don t know

What is the equation for the vertical asymptote of the graph of the function shown O A y 7 O B x 3 O c y 6 0 6 5 3 2 2 3 4 d 6 7 0 2 6

X 2 a vertical line GRAPH GRAPHING NON LINEAR FUNCTIONS use a t chart y b is a horizontal line y 1 11 x

GRAPH ORDERED PAIRS AS X Y Name the quadrants

ind the rate of change for each linear function Time min X 0 1 2 Distance m y 88 66 44 22 3 a decrease of 22 m min b decrease of 22 min m C increase of 22 m min d decrease of 20 m mi

estimate the point slope of the curve at the 00 designated

1 point Find the average rate of change of f x 5x 3 between each of the pairs of points below a Between 2 23 and 5 128 answer b Between a m and p u answer c Between x f x and x h f x h

Write an equation of the line passing through 1 5 and 4 6 Give the answer in standard form

Given f x 17 sin 13x 17 Find an expression that gives all the x intercepts there are an infinite amount of this functi Use the index k as you have done in the problems where 27k is part of the answer Note that exact term is not in this answer It was only given as an example of using k Pleae give an exact answer that means no decimals

Trent has a rich uncle who wishes to give Trent 2 000 on his 17th birthday Trent is smart with his money and decides to put it into a savings account that pays 7 5 interest compounded annually a Write a function to model this situation b How much will Trent s investment be worth when he turns 25 years old Round to the nearest penny

The height y in feet of a ball thrown by a child is y The height y in feet of a ball thrown by a child is 1 2 x 2x 3 y 16 where 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 I c How far from the child does the ball strike the ground feet feet feet The height y in feet of a ball thrown by a child is y 1 16 x2 2x 3 where 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

For the following set of data find the percentage of data within 2 population standard deviations of the mean to the nearest 10th of a percent Data 7 13 14 15 18 19 20 Frequency 1 7 10 12 16 11 8 2 Copy Values for Calculator

linear M 1 13 9 5 3 7 11 Find the equation of the function of the specified type that is the best fit for the given data 3 Check which wariable s should be in your answer Plot the data and the equation