 8.8.3.1: Convert the following quadratic functions to vertex form. Identify ...
 8.8.4.1: Solve the following quadratic equations by factoring. a. x2 2 9 5 0...
 8.8.5.1: Complete these sentences. a. For a quadratic function, the graph of...
 8.8.6.1: . (Graphing program optional.) The equation d 490t 2 50t describes ...
 8.1: For each of the accompanying parabolas, identify the graph as conca...
 8.8.1.1: From the graph of each quadratic function, identify whether the par...
 8.8.2.1: Which of the following quadratics have parabolic graphs that are co...
 8.8.3.2: The daily profit, f (in dollars), of a hot pretzel stand is a funct...
 8.8.4.2: Find the xintercepts for each of the following functions. Will the...
 8.8.5.2: omplete the table for the function y 5 3 2 x 2 x2 . What type of fu...
 8.8.6.2: (Graphing program optional.) The equation d 4.9t 2 1.7t describes t...
 8.2: An electric heater is being designed as a parabolic reflector 6deep...
 8.8.1.2: Using the quadratic function : a. Fill in the values in the table. ...
 8.8.2.2: Match each function to the right with its graph. Explain your reaso...
 8.8.3.3: Find the equations in vertex form of the parabolas that satisfy the...
 8.8.4.3: Factor the quadratic expression and then sketch the graph of the fu...
 8.8.5.3: a. What is the average rate of change of the linear function y 5 3x...
 8.8.6.3: The equation could also be written using distances measured in mete...
 8.3: (Requires graphing program for part (e).) A wood craftsman has crea...
 8.8.1.3: (Graphing program recommended.) On the same graph, plot the followi...
 8.8.2.3: On the same graph, sketch by hand the plots of the following functi...
 8.8.2.4: In each case sketch by hand a quadratic function y (x) with the ind...
 8.8.3.4: Using the strategy of completing the square, fill in the missing nu...
 8.8.4.4: . Construct a quadratic function with zeros at x 5 1 and x 5 2. b. ...
 8.8.5.4: a. Complete the table for the function (x) 5 3x2 2 2x 2 5. b. What ...
 8.8.6.4: The equation could be written using distances measured in feet. Rew...
 8.4: California produces nearly 95% of the processed tomatoes grown in t...
 8.8.1.4: (Graphing program recommended.) On the same graph, plot the three f...
 8.8.2.5: Identify the stretch/compression factor and the vertex for each of ...
 8.8.3.5: (Graphing program optional.) For each quadratic function use the me...
 8.8.4.5: (Graphing program required.) Using a graphing program, estimate the...
 8.8.5.5: Complete the table for the function Q 5 2t 2 1 t 1 1. a. Plot Q 5 2...
 8.8.6.5: Complete the accompanying table. What happens to the average veloci...
 8.5: Construct a function for each parabola g(x) and h(x) in the accompa...
 8.8.1.5: (Graphing program recommended.) Given a point P on a parabola of th...
 8.8.2.6: For each of the following functions, identify the vertex and specif...
 8.8.3.6: (Graphing program optional.) For each quadratic function convert to...
 8.8.4.6: Write each function in factored form, if possible, using integer co...
 8.8.5.6: (Graphing program required.) a. Plot the function h(t) 5 4 1 50t 2 ...
 8.8.6.6: The essay Watching Galileos Learning examines the learning process ...
 8.6: (Technology required to create a bestfit quadratic.) When people m...
 8.8.1.6: Find the coordinates of the vertex for each quadratic function list...
 8.8.2.7: For each of the following quadratic functions, find the vertex (h, ...
 8.8.3.7: Convert the following functions from the abc or standard form to ...
 8.8.4.7: Solve the following equations using the quadratic formula. (Hint: R...
 8.8.5.7: Match the graph of each quadratic function with the graph of its av...
 8.8.6.7: The data from a free fall tape generate the following equation rela...
 8.7: a. Identify the coordinates of the vertex for each of the following...
 8.8.1.7: Given the following focal points, write the equation of a parabola ...
 8.8.2.8: For each quadratic function identify the vertex and specify whether...
 8.8.3.8: (Graphing program required.) Given (x) 5 2x2 1 8x 2 15: a. Estimate...
 8.8.4.8: Solve using the quadratic formula. a. x2 2 3x 5 12 e. b. 3x2 5 4x 1...
 8.8.5.8: Having found the matched pairs of graphs in Exercise 7, explain the...
 8.8.6.8: What would the free fall equation d 490t 2 90t become if d were mea...
 8.8: Find any horizontal intercepts for the following functions. a. y (x...
 8.8.1.8: Find the focal length (the distance from the focal point to the ver...
 8.8.2.9: (Graphing program optional.) Create a quadratic function in the ver...
 8.8.3.9: Write each of the following quadratic equations in function form (i...
 8.8.4.9: Calculate the coordinates of the x and yintercepts for the follow...
 8.8.5.9: Construct a function that represents the average rate of change for...
 8.8.6.9: In the equation d 4.9t 2 500t, time is measured in seconds and dist...
 8.9: a. Construct a quadratic function Q(t) that is concave up and has h...
 8.8.1.9: For each of the following functions, evaluate (2) and (2). a. (x) x...
 8.8.2.10: Transform the function (x) x2 into a new function g(x) by compressi...
 8.8.3.10: Find two different equations for a parabola that passes through the...
 8.8.4.10: Use the discriminant to predict the number of horizontal intercepts...
 8.8.5.10: Construct a function that represents the average rate of change for...
 8.8.6.10: A freely falling object has an initial velocity of 20 ft/sec. a. Wr...
 8.10: Explain why you could (or couldnt) construct a parabola through any...
 8.8.1.10: A designer proposes a parabolic satellite dish 5 feet in diameter a...
 8.8.2.11: Transform the function (x) 3x2 into a new function h(x) by shifting...
 8.8.3.11: Without drawing the graph, list the following parabolas in order, f...
 8.8.4.11: In each part (a) to (e), graph a parabola with the given characteri...
 8.8.5.11: Determine from each of the tables whether you would expect the orig...
 8.8.6.11: (Graphing program optional.) A freely falling object has an initial...
 8.11: Find an equation for the cross section of the parabolic roof of the...
 8.8.1.11: An electric heater is designed as a parabolic reflector that is 5 d...
 8.8.2.12: For the following quadratic functions in vertex form, (x) a(x h)2 k...
 8.8.3.12: Match each of the following graphs with one of following equations....
 8.8.4.12: For each part, draw a rough sketch of a graph of a function of the ...
 8.8.6.12: (Graphing program optional.) Use the information in Exercise 11 to ...
 8.12: (Requires results of 11.) The pool designer wants to mount a light ...
 8.8.1.12: parabolic reflector 3 in diameter and 2 deep is proposed for a spot...
 8.8.2.13: a. Find the equation of the parabola with a vertex of (2, 4) that p...
 8.8.3.13: Marketing research by a company has shown that the profit, P(x) (in...
 8.8.4.13: a. Construct a quadratic function Q(t) with exactly one zero at t 5...
 8.8.6.13: If the equation d 4.9t 2 11t represents the relationship between di...
 8.13: A diver jumps up off the high board, which is 25 feet above the sur...
 8.8.1.13: A slimline fluorescent bulb in diameter needs 1 clearance top and b...
 8.8.2.14: For each part construct a function that satisfies the given conditi...
 8.8.3.14: Tom has a taste for adventure. He decides that he wants to bungeej...
 8.8.4.14: a. Construct a quadratic function P(s) that goes through the point ...
 8.8.6.14: The distance that a freely falling object with no initial velocity ...
 8.14: In the United States a heat wave is a period of three or more conse...
 8.8.1.14: If we know the radius and depth of a parabolic reflector, we also k...
 8.8.2.15: If a parabola is the graph of the equation y a(x 4)2 5: a. What are...
 8.8.3.15: A manager has determined that the revenue R(x) (in millions of doll...
 8.8.4.15: Construct a quadratic function for each of the given graphs. Write ...
 8.8.6.15: (This exercise requires a free fall data tape created using a spark...
 8.15: a. Complete the following table for the function y x2 4x. Average R...
 8.8.1.15: Construct several of your own equations of the form y ax2 and then ...
 8.8.2.16: Construct an equation for each of the accompanying parabolas.
 8.8.3.16: A Norman window has the shape of a rectangle surmounted by a semici...
 8.8.4.16: Complete the following table, and then summarize your findings. i 1...
 8.8.6.16: In the height equation h 300 50t 4.9t 2, time is measured in second...
 8.16: Is each of the statements in 120 true or false? Give an explanation...
 8.8.1.16: For each of the following quadratics with their respective vertices...
 8.8.2.17: Determine the equation of the parabola whose vertex is at (2, 3) an...
 8.8.3.17: A pilot has crashed in the Sahara Desert. She still has her maps an...
 8.8.4.17: Complex number expressions can be simplified by combining the real ...
 8.8.6.17: (Graphing program optional.) The height of an object that was proje...
 8.17: Is each of the statements in 120 true or false? Give an explanation...
 8.8.1.17: Put each of the following quadratics into standard form. a. (x) (x ...
 8.8.2.18: Students noticed that the path of water from a water fountain seeme...
 8.8.3.18: (Requires technology to find a bestfit quadratic.) The accompanyin...
 8.8.4.18: Complex number expressions can be multiplied using the distributive...
 8.8.6.18: (Graphing program optional.) The height of an object that was throw...
 8.18: 1820 refer to the motion equation of an object,h 39.2 9.8t 4.9 t2, ...
 8.8.1.18: Put each of the following quadratics into standard form. a. g(x) (2...
 8.8.3.19: (Graphing program required.) At low speeds an automobile engine is ...
 8.8.4.19: A quadratic function has two complex roots, r1 5 1 1 i and r2 5 1 2...
 8.8.6.19: (Graphing program optional.) Let h 85 490t 2 be a motion equation d...
 8.19: 1820 refer to the motion equation of an object,h 39.2 9.8t 4.9 t2, ...
 8.8.1.19: Determine the dimensions for enclosing the maximum area of a rectan...
 8.8.3.20: (Requires technology to create bestfit functions.) The following d...
 8.8.4.20: The factored form of a quadratic function is y 5 22(x 2 (3 1 i))(x ...
 8.8.6.20: (Graphing program optional.) Let h 85 20t 490t 2 be a motion equati...
 8.20: 1820 refer to the motion equation of an object,h 39.2 9.8t 4.9 t2, ...
 8.8.1.20: A gardener wants to grow carrots along the side of her house. To pr...
 8.8.3.21: A shotput athlete releases the shot at a speed of 14 meters per se...
 8.8.4.21: Use the quadratic formula to find the zeros of the function (x) 5 x...
 8.8.6.21: At t 0, a ball is thrown upward at a velocity of 10 ft/sec from the...
 8.21: For 2130 give an example of a function or functions with the specif...
 8.8.1.21: Which of the following are true statements for quadratic functions?...
 8.8.3.22: (Technology required to generate a bestfit quadratic.) The accompa...
 8.8.4.22: Let (h, k) be the coordinates of the vertex of a parabola. Since th...
 8.8.6.22: The concepts of velocity and acceleration are useful in the study o...
 8.22: For 2130 give an example of a function or functions with the specif...
 8.8.1.22: The management of a company is negotiating with a union over salary...
 8.8.4.23: Put each of the equations into the vertex form, y a(x h) 2 k. a. A ...
 8.8.6.23: The relationship between the velocity of a freely falling object an...
 8.23: For 2130 give an example of a function or functions with the specif...
 8.8.1.23: (Graphing program required for part (c).) A landlady currently rent...
 8.8.4.24: (Graphing program recommended.) a. Write each of the following func...
 8.8.6.24: A certain baseball is at height h 4 64t 16t 2 feet at time t in sec...
 8.24: For 2130 give an example of a function or functions with the specif...
 8.8.1.24: (Graphing program required for part (c).) a. In economics, revenue ...
 8.8.4.25: Find the equation of the graph of a parabola that has the following...
 8.8.6.25: At t 0, an object is in free fall 150 cm above the ground, falling ...
 8.25: For 2130 give an example of a function or functions with the specif...
 8.8.4.26: (Graphing program required for part (b)). In Chapter 3 we determine...
 8.8.6.26: In the Anthology Reading Watching Galileos Learning, Cavicchi notes...
 8.26: For 2130 give an example of a function or functions with the specif...
 8.8.4.27: (Graphing program recommended for part (b)). a. Find the intersecti...
 8.8.6.27: Suppose an object is moving with constant acceleration, a, and its ...
 8.27: For 2130 give an example of a function or functions with the specif...
 8.8.4.28: Market research suggests that if a particular item is priced at x d...
 8.8.6.28: In 1974 in Anaheim, California, Nolan Ryan threw a baseball at just...
 8.28: For 2130 give an example of a function or functions with the specif...
 8.8.4.29: A dairy farmer has 1500 feet of fencing. He wants to use all 1500 f...
 8.8.6.29: An object that is moving horizontally along the ground is observed ...
 8.29: For 2130 give an example of a function or functions with the specif...
 8.8.4.30: In ancient times, after a bloody defeat that made her flee her city...
 8.8.6.30: . (Requires results from Exercise 29.) Find the distance traveled b...
 8.30: For 2130 give an example of a function or functions with the specif...
 8.8.6.31: An object is observed to have an initial velocity of 200 m/sec and ...
 8.31: Is each of the statements in 3140 true or false? If a statement is ...
 8.8.6.32: You may have noticed that when a basketball player or dancer jumps ...
 8.32: Is each of the statements in 3140 true or false? If a statement is ...
 8.8.6.33: Old Faithful, the most famous geyser at Yellowstone National Park, ...
 8.33: Is each of the statements in 3140 true or false? If a statement is ...
 8.34: Is each of the statements in 3140 true or false? If a statement is ...
 8.8.6.34: A vehicle trip is composed of the following parts: i. Accelerate fr...
 8.35: Is each of the statements in 3140 true or false? If a statement is ...
 8.8.6.35: In general, for straight motion of a vehicle with constant accelera...
 8.36: Is each of the statements in 3140 true or false? If a statement is ...
 8.37: Is each of the statements in 3140 true or false? If a statement is ...
 8.38: 3840 refer to the motion equation of an object, h 80 64t 16t2, desc...
 8.39: 3840 refer to the motion equation of an object, h 80 64t 16t2, desc...
 8.40: 3840 refer to the motion equation of an object, h 80 64t 16t2, desc...
Solutions for Chapter 8: QUADRATICS AND THE MATHEMATICS OF MOTION
Full solutions for Explorations in College Algebra  5th Edition
ISBN: 9780470466445
Solutions for Chapter 8: QUADRATICS AND THE MATHEMATICS OF MOTION
Get Full SolutionsSince 180 problems in chapter 8: QUADRATICS AND THE MATHEMATICS OF MOTION have been answered, more than 1870 students have viewed full stepbystep solutions from this chapter. Explorations in College Algebra was written by Sieva Kozinsky and is associated to the ISBN: 9780470466445. Chapter 8: QUADRATICS AND THE MATHEMATICS OF MOTION includes 180 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Explorations in College Algebra, edition: 5.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.
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