 7.1.2: In Exercises 16, match the equation with one of thegraphs (a)(f), w...
 7.1.3: In Exercises 16, match the equation with one of thegraphs (a)(f), w...
 7.1.4: In Exercises 16, match the equation with one of thegraphs (a)(f), w...
 7.1.5: In Exercises 16, match the equation with one of thegraphs (a)(f), w...
 7.1.6: In Exercises 16, match the equation with one of thegraphs (a)(f), w...
 7.1.7: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.8: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.9: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.10: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.11: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.12: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.13: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.14: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.15: Find an equation of a parabola satisfying the givenconditions. Vert...
 7.1.16: Find an equation of a parabola satisfying the givenconditions. Vert...
 7.1.17: Find an equation of a parabola satisfying the givenconditions. Focu...
 7.1.18: Find an equation of a parabola satisfying the givenconditions. Focu...
 7.1.19: Find an equation of a parabola satisfying the givenconditions.Focus...
 7.1.20: Find an equation of a parabola satisfying the givenconditions. Focu...
 7.1.21: Find an equation of a parabola satisfying the givenconditions. Focu...
 7.1.22: Find an equation of a parabola satisfying the givenconditions. Focu...
 7.1.23: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.24: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.25: Find the vertex, the focus, and the directrix. Then drawthe graph.x...
 7.1.26: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.27: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.28: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.29: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.30: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.31: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.32: Find the vertex, the focus, and the directrix. Then drawthe graph. ...
 7.1.33: Satellite Dish. An engineer designs a satellitedish with a paraboli...
 7.1.34: Flashlight Mirror. A heavyduty flashlight mirrorhas a parabolic cr...
 7.1.35: Ultrasound Receiver. Information Unlimiteddesigned and sells the Ul...
 7.1.36: Spotlight. A spotlight has a parabolic cross sectionthat is 4 ft wi...
 7.1.37: Consider the following linear equations. Withoutgraphing them, answ...
 7.1.38: Consider the following linear equations. Withoutgraphing them, answ...
 7.1.39: Consider the following linear equations. Withoutgraphing them, answ...
 7.1.40: Consider the following linear equations. Withoutgraphing them, answ...
 7.1.41: Consider the following linear equations. Withoutgraphing them, answ...
 7.1.42: Consider the following linear equations. Withoutgraphing them, answ...
 7.1.43: Consider the following linear equations. Withoutgraphing them, answ...
 7.1.44: Consider the following linear equations. Withoutgraphing them, answ...
 7.1.45: Find an equation of the parabola with a verticalaxis of symmetry an...
 7.1.46: Find an equation of a parabola with a horizontalaxis of symmetry an...
 7.1.47: Use a graphing calculator to find the vertex, the focus,and the dir...
 7.1.48: Use a graphing calculator to find the vertex, the focus,and the dir...
 7.1.49: Suspension Bridge. The cables of a 200ft portionof the roadbed of ...
Solutions for Chapter 7.1: The Parabola
Full solutions for College Algebra: Graphs and Models  5th Edition
ISBN: 9780321783950
Solutions for Chapter 7.1: The Parabola
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra: Graphs and Models, edition: 5. Since 48 problems in chapter 7.1: The Parabola have been answered, more than 26121 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. College Algebra: Graphs and Models was written by and is associated to the ISBN: 9780321783950. Chapter 7.1: The Parabola includes 48 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Iterative method.
A sequence of steps intended to approach the desired solution.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

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.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).