Quadratic equations Questions and Answers

Consider the set 2 6 1 1 0 6 2 0 1 which is a basis for R Construct anorthogonal basis of R whose first element is 2 6 1 Then find the coordinates of the vector 2 5 0 with respect to the new basis

What step will solve the following equation 6 5 m 60

For the equation x y 4x 8y 16 0 do the following a Find the center h k and radius r of the circle b Graph the circle c Find the intercepts if any a The center is Type an ordered pair The radius is r b Use the graphing tool to graph the circle Click to enlarge graph c Find the intercepts if any Select the correct choice below and if necessary fill in the answer box to complete your choice OA The intercept s is are Type an ordered pair Use a comma to separate answers as needed Type exact answers for each coordinate using radicals as needed B There is no intercept

Find the intercepts and graph the equation by plotting points 15x 16y 240 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The intercept s is are Type an ordered pair Use a comma to separate answers as needed OB There are no intercepts Use the graphing tool to graph the equation Click to enlarge graph

meisects the cle in a single point called the point of tangency Find the standard form of the equation of the circle with center 7 8 and tangent to the y axis The standard form of the equation of the circle with center 7 8 and tangent to the y axis is Type an equation D

Find the following for the function f x 4x 3x 2 a f 0 b f 3 c f 3 e f x f f x 3 g f 5x Simplify your answer Simplify your answer Simplify your answer Simplify your answer Simplify your answer f f x 3 Simplify your answer g f 5x Simplify your answer h f x h Simplify your answer a f 0 b f 3 c f 3 d f x e f x d f x h f x h

g x Simplify your answer Use integers or fractions for any numbers in the expression

1 Use the equation Q 5x 3y and the following constraints 3y 625x y 3 4x 8 a Maximize and minimize the equation Q 5x 3y b Suppose the equation Q 5x 3y was changed to Q 52 3y describe how the maximum and minimum w change in the new equation compared to the original equation and explain why you think it is that way B U Font Family AAAF E

Determine if the relation is a function Domain each person in a town Correspondence each person s uncle Range a set of males Is this relationship a function O No OYes

Consider the following graph a What is the amplitude b What is the period 3 MMMM TT12 TV4 0 TV4 3 4 1 114 c Find an equation involving sine 4 d Find an equation involving cosine 3

Which equation best represents the following function 2 Oy x 1 2 6 Oy 2x 1 Oy 2 1 Oy x 2 1 x

Solve this question using power series method 1 25 pt Solve the equation y x sy s ds by presenting two linearly independent solutions

a Find the slope of the line through 16 8 and 18 16 b Based on the slope indicate whether the line through the points rises from left to right falls from left to right is horizontal or is vertical a Select the correct choice below and if necessary fill in the answer box to complete your choice OA The slope is Type an integer or a simplified fraction OB The slope is undefined b Choose the correct answer below OA The line is vertical OB The line through the points rises from left to right C The line through the points falls from left to right OD The line is horizontal

Name 6 If f x 3x 9 and g x x find the following a f 2 f x 3x 9 f 2 3 2 9 6 9 15 c x if f x 0 F X 3x 9 f x 0 3x 9 0 Date 3x 9 x 3 b g 2 f x 3x 9 g x x 9 0 d g m Hour 9 2 2 9

22 Identify the standard form of the equation of a line which has a slope of and goes through 2 3 x 2y 4 2x y 4 Ox 2y 4 2x y 4

Complete the slope intercept form equation of the line with slope that passes through point 0 2 Complete the equation for y in the space below do not enter y E

11 The focal length of a magnifying glass is modeled by the equation where t is the distance from the eye to the glass s is the distance from the glass to the object viewed a f is the focal length of the glass Calculate the distance from the glass to the object s if t 13 81 and f 8 7 and A nswer

18 On a separate sheet graph the set of ordered pairs on a coordinate plane Then use the vertical line test to determine if each relation is a function 1 4 2 3 2 2 4 2 1 3 Make sure to check the feedback for this question to see if your graph matches the graph we have prepared for you It is not a function It is a function

13 Solve the following equation by graphing 12 4 Find the solution algebraically to verify your graph Find the solution and any values for that make the graph undefined O Solution a 48 undefined values for a 12 x 0 O Solution x 24 undefined values for r x 12 x 0 O Solution x 48 undefined values for x 12 X O Solution no solution undefined values for r x 12

12 State the number of solutions without graphing 18x 3y 15 30x 36 3y OTwo solutions O One solution O No solutions

7 Solve the exponential equation 16 4 2 1 X x

Carl is making a garden that is twice as long as it is wide He wants to cover 271 square feet with the garden Which equation best represents the situation if x represents the length of the garden

6 Rewrite using only positive exponents w 352 O O

5 Identify the slope x intercept and y intercept of the line whose equation is 2x y 8 Om 2 x intercept 4 y intercept 8 Om x intercept 4 y intercept 8 Om 2 x intercept 4 y intercept 8 Om 1 x intercept 4 y intercept

2 Solve the rational equation off 16 OO Or 1 0 x 0 1 1 1 X x 1 1

19 Which of the following is an inverse variation Oy 5 2 Ox 5y 0 x Oy 5x

24 Simplify abe ac 10 12 10 a c O abc ac c abc O 00 O None of the answers shown is a simplification of the orig

9 Given the formula V Ah solve for A 3h O Vh 3 O 3V 31h

7 The most simplified form of 8 32 is O 32 y 3x 12zy2 O 32 y 3x 12x7y5 9 32x y5 3x y 12x7y5 32x6y5 3x7y

11 Simplify O 3x 63x 2 49 O9x 63x 22 49 O O92 63x 49 3x 63x 49 3x 62 20 7 O None of the answers shown are corre

et P be the vector space of all polynomials of degree 2 or less and let H be the subspace spanned by 18x 9x 14 9x 4x 7 and 18x 7x 14 a The dimension of the subspace H is b Is 18x 9x 14 9x 4x 7 18x 7x 14 a basis for P choose c A basis for the subspace H is Enter a polynomial or a comma separated list of polynomials Be sure you can explain and justify your answer

For the functions f x x and g x a fog x and its domain b gof x and its domain a fog x Do not rationalize the denominator 1 x 2 Its domain is Type your answer in interval notation b gof x Do not rationalize the denominator Its domain is Type your answer in interval notation find the following

In Exercises 11 18 a write the linear function f such that it has the indicated function values and b sketch the graph of the function 11 f 1 4 f 0 6 12 f 3 8 f 1 2

Without graphing determine whether the following equation has a graph that is symmetri with respect to the x axis the y axis the origin or none of these x y 19 Select all that apply A x axis B origin C y axis D none of these

Find the slope and y intercept of the given line and graph it 7y 8x The slope of the line is Simplify your answer Type an integer or a fraction What is the y intercept Type an ordered pair Use the graphing tool to graph the line Click to enlarge 10 8 6 4 2 Ay 140 8 6 4 2 2 4 6 8 6 2

range Use the graphing tool to graph the equation Click to enlarge graph What is the domain Select the correct choice below and if necessary fill in the answer box to complete your choice OA The domain in interval notation is Type your answer in interval notation B The domain is a value or list of distinct values Type an integer or a simplified fraction Use a comma to separate answers as needed What is the range Select the correct choice below and if necessary fill in the answer box to complete your choice OA The range in interval notation is Type your answer in interval notation B The range is a value or list of distinct values Type an integer or a simplified fraction Use a comma to separate answers as needed 10

For the equation y x 2 a create a table with ordered pairs that are solutions of the equation and b graph the equation a Complete the following table of ordered pairs that are solutions of the equation X 1 0 1 2 y b Use the graphing tool to graph the equation Click to enlarge graph Ay 20 16 12 ob 4 8 12 16 20

Solve the logarithmic equation Be sure reject any value of x that is not in the domain of the original logarithmic expression Give an exact answer Then use a calculator to obt decimal approximation correct to two decimal places for the solution In x 6 1 Rewrite the given equation without logarithms Do not solve for x Solve the equation What the exact solution Select the correct choice below and if necessary fill in the answer box to complete your choice O A The solution set is Type an exact answer Type your answer using exponential notation

Let f x x 13 and g x 17 x Perform the composition or operation indicated fg 9 fg 9

Find the function g x whose graph can be obtained by translating the graph of f x 4x 3 up 6 units and to the right 2 units Write the function g x Tyne an expression using x as the variable

lowing linear function Give the domain and range Identify whether it is a constant function f x x 3 What is the domain Select the correct choice below and fill in the answer box to complete your choice graph OA The domain in interval notation is Type your answer in interval notation OB The domain is a value or list of distinct values Type an integer or a simplified fraction Use a comma to separate answers as needed What is the range Select the correct choice below and fill in the answer box to complete your choice OA The range is a value or list of distinct values Type an integer or a simplified fraction Use a comma to separate answers as needed OB The range in interval notation is Type your answer in interval notation Is f x x 3 a constant function Yes O No 11

Graph the following piecewise function f x 2 if x 1 1 if x 1 Choose the correct graph below O A X OB FI O C O D Ay

Find k so that the line through 1 5 and k 9 is a parallel to 5y 4x 3 b perpendicular to 4y 3x 5 If the line is parallel to 5y 4x 3 then k If the line is perpendicular to 4y 3x 5 then k

Give a rule of the piecewise defined function Give the domain and the range O A f x if x if x2 O A The domain is OB The domain is 5 4 3 What is the rule Select the correct choice below and fill in the answer boxes within your choice OB f x Use a comma to separate answers as needed Type your answer in interval notation O A The range is 5 Use a comma to separate answers as needed B The range is Tuno your answer in interval notation Ay 4 3 2 What is the domain Select the correct choice below and fill in the answer box within your choice if x 2 if x o What is the range Select the correct choice below and fill in the answer box within your choice

se the graph to solve the equation and inequalities a 2x x 3 b 2x x 3 2x2 x 3 c 5 T 3 2 1 2 Y 2x 2 2 3 5 2 3 5

a Use slope intercept form to write an equation of the line that passes through the given point and has the given slope b Write the equation using function notation where y f x 4 2 m 5 Part 0 2 Part 1 of 2 The equation of the line in slope intercept form is 0 0

Find the polynomial of degree 4 whose graph is shown 12 8 12 4 00 12 co 8 12

Part 2 of 4 k x 3 Part 3 of 4 g x Part 4 of 4 10 3x 3 OOO neither linear nor constant linear constant neither linear nor constant linear constant neither linear nor constant linear X X

Determine the slope of the line m 2 19 2 3

Determine the domain and range of the function 3 2 3 2 H 2 3 y T 2 3 O A V