 107.1: y = 5 y2 = x2 + 9
 107.2: y  x = 1 x2 + y2 = 25
 107.3: 3x = 8y2 8y2  2x2 = 16
 107.4: 5x2 + y2 = 30 9x2  y2 = 16
 107.5: CELL PHONES A person using a cell phone can be located in respect t...
 107.6: x + y < 4 9x2  4y2 36
 107.7: x2 + y2 < 25 4x2  9y2 < 36
 107.8: y = x + 2 y = x
 107.9: y = x + 3 y = 2x2
 107.10: x2 + y2 = 36 y = x + 2
 107.11: y2 + x2 = 9 y = 7  x
 107.12: x_ 2 30 + y2 _ 6 = 1 x = y
 107.13: x_ 2 36  y2 _ 4 = 1 x = y
 107.14: 4x + y2 = 20 4x2 + y2 = 100
 107.15: y + x2 = 3 x2 + 4y2 = 36
 107.16: x2 + y2 = 64 x2 + 64y2 = 64
 107.17: y2 + x2 = 25 y2 + 9x2 = 25
 107.18: y2 = x2  25 x2  y2 = 7
 107.19: y2 = x2  7 x2 + y2 = 25
 107.20: x + 2y > 1 x2 + y2 25
 107.21: x + y 2 4x2  y2 4
 107.22: x2 + y2 4 4y2 + 9x2 36
 107.23: x2 + y2 < 36 4x2 + 9y2 > 36
 107.24: y2 < x x2  4y2 < 16
 107.25: x2 y y2  x2 4
 107.26: Graph each system of equations. Use the graph to solve the system. ...
 107.27: Find the point(s) of intersection of the orbits of Pluto and the co...
 107.28: Will the comet necessarily hit Pluto? Explain.
 107.29: Where do the graphs of y = 2x + 1 and 2x2 + y2 = 11 intersect?
 107.30: What are the coordinates of the points that lie on the graphs of bo...
 107.31: ROCKETS Two rockets are launched at the same time, but from differe...
 107.32: ADVERTISING The corporate logo for an automobile manufacturer is sh...
 107.33: Solve each equation for y.
 107.34: Use a graphing calculator to estimate the intersection points of th...
 107.35: Compare the orbits of the two satellites.
 107.36: two parabolas that intersect in two points
 107.37: a hyperbola and a circle that intersect in three points
 107.38: a circle and an ellipse that do not intersect
 107.39: a circle and an ellipse that intersect in four points
 107.40: a hyperbola and an ellipse that intersect in two points
 107.41: two circles that intersect in three points
 107.42: REASONING Sketch a parabola and an ellipse that intersect in exactl...
 107.43: OPEN ENDED Write a system of quadratic equations for which (2, 6) i...
 107.44: no solutions
 107.45: one solution
 107.46: two solutions
 107.47: three solutions
 107.48: four solutions
 107.49: Which One Doesnt Belong? Which system of equations is NOT like the ...
 107.50: Writing in Math Use the information on page 603 to explain how syst...
 107.51: ACT/SAT How many solutions does the system of equations x2 _ 52  y...
 107.52: REVIEW Given: Two angles are supplementary. One angle is 25 more th...
 107.53: x2 + y2 + 4x + 2y  6 = 0
 107.54: 9x2 + 4y2  24y = 0
Solutions for Chapter 107: Solving Quadratic Systems
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 107: Solving Quadratic Systems
Get Full SolutionsSince 54 problems in chapter 107: Solving Quadratic Systems have been answered, more than 56790 students have viewed full stepbystep solutions from this chapter. Chapter 107: Solving Quadratic Systems includes 54 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. This expansive textbook survival guide covers the following chapters and their solutions.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

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

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

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.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Solvable system Ax = b.
The right side b is in the column space of A.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.