Quadratic equations Questions and Answers

0 1 pt 2 Details 3 Use synthetic division to divide x 4x 4x 6 by x 1 Th 1 4 4

0 1 pt 2 Details The polynomial of degree 3 P x has a root of multiplicity 2 at x 4 and a root of multiplicity 1 at x 5 The y intercept is y 56 Find an equation for P x P x

pt Consider the function P x x 7 x 4 The y intercept is the point The x intercept s is are the point s As x y etails As y

Given P x x x 16x16 find the zeros 3 real and non real of P The zeros are Write P in factored form as a product of linear factors Be sure to write the full equation including P x

Write an equation any form for the quadratic graphed below 5 4 3 2 X 5 4 3 2 1 y 1 2 3 4 5 1 2 3 4 5

ve the equation for the given variable Show your 2E V2iE

Graph the polynomial function Factor first if the expression is not in factored form f x x x 2 x 4 Choose the correct graph below O A 500 O B O C 500 O D 500

Find an equation for the rational function graph Choose the correct function for the graph O O O f x f x f x f x x 3 X 5 X 3 x x 5 x x 5 x 3 X x 3 x 5 2 1 1 F3 3 15

For the given equation and graph of the quadratic function do the following Complete parts a through e f x x 3 4 a Give the domain and range The domain is Type your answer in interval notation The range is Type your answer in interval notation b Give coordinates of the vertex The vertex is Type an ordered pair c Give the equation of the axis of symmetry The axis of symmetry is x d Find the y intercept s The y intercept s is are Type an ordered pair Use a comma to separate answers as needed e Find the x intercept s The x intercept s is are T ored noir Leo 2 comma to 19 10 8 642 Ay BH 6 B 10

Find all complex zeros of the polynomial function Give exact values List multiple zeros as necessary f x x5 6x4 17x 38x 60x 40 All complex zeros are Type an exact answer using radicals and i as needed Use a comma to separate answers as needed

Solve the rational inequality Give the solution set in interval notation x 4x 5 x 4x 4 0 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Type your answer in interval notation Use integers or fractions for any numbers in the expression There is no solution

3 Analyze the polynomial function f x x 0 3x 1 3677x 0 38229 Complete parts a through h Type an integer or decimal rounded to two decimal places as needed Use a comma to separate answers as needed d Use a graphing utility to create a table to find points on the graph around each x intercept Complete the table below X 2 1 0 1 2 Y x 0 3x 1 3677x 0 38229 Y 4

Use a graphing utility to approximate the local maximum value and local minimum value of the function f x 0 3x 0 6x 4x 4 for 6 x 4 Using a graphing utility graph the function for 6 x 4 and 25 y 10 Choose the correct graph below OA Q OB The local maximum is y and it occurs at x Round to the nearest hundredth as needed The local minimum is y and it occurs at x G O C Q Q

Use the graph to the right to find the angle with the same secant as sec 30 The angle is Type your answer in degrees 76 Ay 2

ind a vector function that represents the curve of intersection of the surfaces y 9 and x z 10 Sketch a graph of the two surfaces and their curve of intersection

Find the polynomial function f x having the graph below a b 1 0 Ans a f x 2 0 3 8 3 0 0 12 N 1 0 2 0 25 x Ans b f x

Question 2 8 points For the polynomial function f x 24x 80x 82x 24 a list all possible rational zeros b find all rational zeros

Graph each rational function a c below Make sure to include all asymptotes x and y intercepts Use dashed lines for asymptotes on the graph If there is no asymptote stat so Also choose appropriate scale for the graphs a f x VA is are HA is OA is x 2x 2x 1 y X X Y

b f x VA is are HA is OA is x 3 x 5 x 1 x 4 X Y y

Find a polynomial function f x of least degree having only real coefficients and zeros as given Assume multiplicity 1 unless otherwise stated Do not leave answer in factor form expand and simplify the polynomial a 2 i and 3 with multiplicity 2 b 0 i and 2 i

Use the remainder theorem and synthetic division to find f k for the given value of k f x 2x 14x 13x 9 k 6 f 6

The graph of the derivative F x of F x is given below 0 1 2 If F 0 4 what is F 6 F 6 F x 3 4 01 5 6

Find a polynomial equation with real coefficients that has the given zeros 1 5i and 1 5i

Analyze the polynomial function f x x 3 x 7 using parts a through e The graph of f behaves like y for large values of Ix b Find the x and y intercepts of the graph of the function The x intercept s is are Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once The y intercept is Simplify your answer Type an integer or a fraction c Determine the zeros of the function and their multiplicity Use this information to determine whether the graph crosses or touches the x axis at each x inter The zero s of f is are Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once so the graph of f The lesser zero is a zero of multiplicity the x axis at x the x axis at x The greater zero is a zero of multiplicity so the graph of f

Use synthetic division to perform the following division x 3x 5x 14x X 2 x 3x 5x 14x Simplif x 2 0

Which rational function has the given graph O A O C R x 2x 25 R x 2x 25 2 10 8 6 4 2 4 2 4 6 8 10 B D I R x R x 2x x 25 2x x 25

Form a polynomial whose real zeros and degree are given Zeros 5 1 1 2 degree 4 Type a polynomial with integer coefficients and a leading coefficient of 1 f x Simplify your answer

1 point For the function f x what are the vertical asymptotes Give a list of the x values of the asymptotes separated by commas x 3 5 4 5 What is the horizontal asymptote x 0 3 5 4 5 What is the y intercept 4x 5x 3 5x 4 y 0 What are the x intercepts Give a list of the x values of the x intercepts separated by commas 0

10 Two friends meet up at a Barnes Noble When they leave one friend drives north at a constant speed of 32 mph and the other friends drives west at a speed of 36 mph When the friends have each driven for 15 minutes at what rate is the distance between them changing Hint draw a triangle

Factor f x 6x 19 6i x 16 7i x 4 2i into linear factors given that k 2 i is a zero Hint Use Synthetic Division

6 8 pes Consider AABC and ADEF where BCEF and 28 ZE What other corresponding parts would have to be congruent for the triangles to be congruent by a SSS b SAS c ASA E 4 AAS

Jayne stopped to get gas before going on a road trip The tank already had 4 gallons of gas in it Which equation relal the total amount of gasoline in the tank y to the number of gallons that she put in the tank x y 4 x y x 4 y 4 x y x 4

45 Find the sum of the geometric series in which a 972 n 5 and r This question is weighted four times as heavily as the other questions In order to receive full or partial credit for th answer or show your work O 732 1264 984 O 1452

35 The length of a rectangle is 6 inches less than its width If the area of the rectangle is 81 square inches write an equation for the situation This question is weighted four times as heavily as the other questions In order to receive full or partial credit for this question use the space provided to justify your answer or show your work O w w 6 81 Ow 6 81 Ow 6 81 w w 6 81

29 Solve for a 24 2 by graphing Find the solution algebraically to verify your graph O x 8 O x 9 O x 5 Ox 14 4 30 Identify the number that needs to be added to both sides of the equation x 14x 15 to complete the square

27 Determine if the equation is a linear equation 3y 14 x O yes O no 4 28 Simplify 20 4g 7g 35 7 g 5 4g 20 07 0

23 State the type of system of equations 11a 11y 143 4x 5y 13 O Inconsistent O Consistent and dependent O Consistent and independent O None of the above 24 Evaluate 2x2y5 if x 3 and y 2 EN English United States

O two real roots O three real roots no real roots 47 Factor 15a 10x 5a O 5x 3x 2x O5x 3x 2x 1 O 5x 3x 1 x 1

24 Evaluate 2x2y if x 3 and y 2 This question is weighted four times as heavily as the other questions In order to receive full or partial credit for th answer or show your work O 576 192 O 576 192 1 1

20 Find the first five terms in the geometric sequence a 15 r 15 10 5 0 5 15 75 375 1875 9375 3 3 3 O 15 3 5 125 O 15 151 152 153 15 21 To graphically solve the quadratic equation x 2x 11 6

18 Simplify the following expression 9x 3x 7 3x 1 O 12x 3x 7 O 12x 3x 7 12x 3x 7 O 12x 3x O 12x 3 7 19 Solve the following equation by graphing 3 x 12

Tr 21 To graphically solve the quadratic equation x 2x 11 6 all of these are practical ways to solve the quadratic graphically O Use the quadratic formula letting a 1 b 2 and c 17 let y x 2x 11 and y2 6 Find the points at which they intersect Set the equation y x 2x 11 equal to 0 Then find the roots of the graph the glong interpent form for the countion of the

22 Find the slope intercept form for the equation of the line which passes through the point 1 14 and has a slope of 2 4 Oy 2x 12 Oy 2x 16 O y 2x 16 2 O y 2x 12

14 Find the maximum value for the equation C 3x 4y given the following constraints x 0 y 20 x y 8 This question is weighted four times as heavily as the other questions In order to receive full or partial credit for answer or show your work O 48 O 24 O 0 O 32

10 Use the table below to find a prediction equation to show how the number of hours worked relates to the This question is weighted four times as heavily as the other questions In order to receive full or partial answer or show your work Hours 2 5 8 Savings 32 50 68 Oy x 32 Oy 6x 20 Oy 6x 32 1 x 20 y 10 15 80 110

8 Find the slope of a line which is perpendicular to the line that has an equation of 3a y 5 0 4 OF 4

6 Rewrite using only positive exponents 7 x y929 343a 125 O125 20 343x y O O125 3432 125x y 343 2 4

5 Which expression can be substituted for a in the top equation of the system below to solve the system by substitution 4x 8y 4 a 4y 8 O8 4y O4y 8 O8y 4 04 8y

For the following bonds find a the interest b the cost of the bond and c the annual yield 1 A 1 000 GE Global bond at 80 5 that pays 6 interest 2 A 10 000 California Municipal bond at 102 5 that pays 5 interest

What is the value of x y 00 75 N 12 16