-3 -2 -1 0 1 2 3 4 -45 -16 -3 10 -1 0 9 32 The following represent a set of points that lie on the graph of a function. Determine the equation of the polynomial using an algebraic method

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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note: follow the solution format of the sample equation given in the second picture

Quiz: Polynomial Equation
Use finite differences to determine the equation for the
polynomial corresponding to the given table of values.
X
y
-3
-2 -4
-1
0
0 6
8
123
O
AJA
-4
4
JIN
2
-8
8
NJ
2
I
10:
-24-16
-24
3
fax) = -x²³ - 2x² + 5x 46
? ? ? ?
1
f(x) = ax³+ bx² + cx +d
3² = 3x2x1 = -1
a =
H
31
f(x) = -x³ + bx² + cx +d
f(0) = d = 6
2
-(-1)³ + b(-1)² + ((-1) + 6
f(-1) =
0 = 1 + b = c +6=b-C+75
f(¹) =
3=
-7=
(+2) 2b = -4
b=-2
−1+b+c+6 = 8
b+c
b-c
20=10
c = 5
(2)
Transcribed Image Text:Quiz: Polynomial Equation Use finite differences to determine the equation for the polynomial corresponding to the given table of values. X y -3 -2 -4 -1 0 0 6 8 123 O AJA -4 4 JIN 2 -8 8 NJ 2 I 10: -24-16 -24 3 fax) = -x²³ - 2x² + 5x 46 ? ? ? ? 1 f(x) = ax³+ bx² + cx +d 3² = 3x2x1 = -1 a = H 31 f(x) = -x³ + bx² + cx +d f(0) = d = 6 2 -(-1)³ + b(-1)² + ((-1) + 6 f(-1) = 0 = 1 + b = c +6=b-C+75 f(¹) = 3= -7= (+2) 2b = -4 b=-2 −1+b+c+6 = 8 b+c b-c 20=10 c = 5 (2)
-3
-2
-1
0
1
2
3
4
-45
-16
-3
0
-1
0
9
32
The following represent a set of points that lie on the graph of a function. Determine the equation of the polynomial using an
algebraic method
Transcribed Image Text:-3 -2 -1 0 1 2 3 4 -45 -16 -3 0 -1 0 9 32 The following represent a set of points that lie on the graph of a function. Determine the equation of the polynomial using an algebraic method
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