For Exercises 27-34, an equation of a parabola x 2 = 4 p y or y 2 = 4 p x is given. a. Identify the vertex, value of p , focus, and focal diameter of the parabola. b. Identify the endpoints of the latus rectum, c. Graph the parabola. d. Write equations for the directrix and axis of symmetry x 2 = − 4 y
For Exercises 27-34, an equation of a parabola x 2 = 4 p y or y 2 = 4 p x is given. a. Identify the vertex, value of p , focus, and focal diameter of the parabola. b. Identify the endpoints of the latus rectum, c. Graph the parabola. d. Write equations for the directrix and axis of symmetry x 2 = − 4 y
Solution Summary: The author compares the values of p, vertex, focus, and focal diameter of the parabola to the standard form of equation.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY