For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x -intercept(s). d. Determine the y -intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) g x = − x 2 + 2 x − 4
For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x -intercept(s). d. Determine the y -intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) g x = − x 2 + 2 x − 4
Solution Summary: The author compares the given function with the parabolic function to determine the vertex of the parabola for the function.
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering-
Al musayab
Subject :Numerical Analysis
Stage:Third
Time: 2 hour
Automobile Department
Date:26-3-2023
nd
1st month exam/2"
semester (2022-2023)
Note: Answer all questions, all questions have same degree.
Q1: Use Newton's method to find solutions to the system with two
step Take (X,Yo)=(8,10).
{
x35x2 + 2xy + 13 = 0
x3 + x²-14x-y-19=0
Q2/:Solve the system by Gauss-Seidel iterative method.(Perform only
three iterations).
8x-3y+2z-20
4x+11y-z-33
6x+3y+12z-35
03/:Curve fit the data using a power function
X
2
4
8
5
6
0.7500
0.1875
0.1200
0.0833
0.0469
University of Babylon
Faculty of Engineering-AlMusyab
Automobile Eng. Dep.
Year: 2022-2023,
2nd Course, 1 Attempt
Stage: Third
Subject: Numerical
Analysis
Date: 2023\\
Time: 3 Hour
dy
= x + yl
Q5-A: Using Euler's method, find an approximate value
of (y) corresponding to (x=0.3),given that[-
and [y=1 when x=0].(taking h=0.1).
dx
(10 M)
Q5-B Find a root of an equation[f(x)=x-x-1] using
Newton Raphson method to an accuracy of &=0.
(10 M)
Q6:Using Newton's divided differences formula, evaluate
f(8) given:
X
4
58 7 103 11
13
Y=f(x)
48
100
900
294
1210
2028
(20 M)
Lexaminer:
Examiner:
Good luck
W
Head of Department:
Explain the conditions under which the Radius of Convergence of the Power Series is a "finite positive real number" r>0
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