I need help with this Linear Algebra problem, I also put an example, I suspect this is somewhat whatthey want in this question, but I am nor sure and need help starting it. How should I approach this problem?Thank you? 37. Calculus The graph of a parabola passes throughthe points (0, 1) and (2, 2) and has a horizontal tangentline at (2). Find an equation for the parabola andsketch its graph. (-2, 3)10-8-(-1,5)3Figure 1.54-(0, 1)(2, 10)(1,4)EXAMPLE 2 Polynomial Curve FittingSee LarsonLinearAlgebra.com for an interactive version of this type of example.Find a polynomial that fits the points(-2, 3), (-1, 5), (0, 1), (1, 4), and (2, 10).SOLUTIONYou are given five points, so choose a fourth-degree polynomial functionp(x) = a₁ + a₁x + α₂x² + α3x³ + à¸xª.Substituting the points into p(x) produces the system of linear equations shown below.ao - 2a₁ +4a₂-8a3 + 16a4 3ao-a₁ + a₂ -az +a₁ =5ao1ao + a₁ + a₂ + az +a4 =4a + 2a₁ + 4a₂ + 8a3 + 16a4 = 10==The solution of these equations isa₁ = 1, a₁ = -√, A₂ = 24, az = ³/1, A4 = -=-12-17Figure 1.5 shows the graph of p.which means the polynomial function isp(x) = 1 − ²x + 101x² + x³ – 17x4.-

Answered: Image /qna-images/answer/ae17d1ca-882d-4083-8717-19edc1acd624.jpg

Answered: 37. Calculus The graph of a parabola…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

I need help with this Linear Algebra problem, I also put an example, I suspect this is somewhat whatthey want in this question, but I am nor sure and need help starting it. How should I approach this problem?

Thank you?

37. Calculus The graph of a parabola passes through
the points (0, 1) and (2, 2) and has a horizontal tangent
line at (2). Find an equation for the parabola and
sketch its graph.

(-2, 3)
10-
8-
(-1,5)
3
Figure 1.5
4-
(0, 1)
(2, 10)
(1,4)
EXAMPLE 2 Polynomial Curve Fitting
See LarsonLinearAlgebra.com for an interactive version of this type of example.
Find a polynomial that fits the points
(-2, 3), (-1, 5), (0, 1), (1, 4), and (2, 10).
SOLUTION
You are given five points, so choose a fourth-degree polynomial function
p(x) = a₁ + a₁x + α₂x² + α3x³ + à¸xª.
Substituting the points into p(x) produces the system of linear equations shown below.
ao - 2a₁ +4a₂-8a3 + 16a4 3
ao-
a₁ + a₂ -
az +
a₁ =
5
ao
1
ao + a₁ + a₂ + az +
a4 =
4
a + 2a₁ + 4a₂ + 8a3 + 16a4 = 10
=
=
The solution of these equations is
a₁ = 1, a₁ = -√, A₂ = 24, az = ³/1, A4 = -
=-12-17
Figure 1.5 shows the graph of p.
which means the polynomial function is
p(x) = 1 − ²x + 101x² + x³ – 17x4.
-

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

Expert Solution