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Chapter 5: Q32E (page 247)

Fit a quadratic polynomial to the data points (1,0) , (2,0) , (3,0) using least square. Sketch the solution.

Short Answer

Expert verified

The solution is f(x)=6.75x2-28.35x+25.35.

Step by step solution

01

Step:1 Explanation of the solution

Consider the data points as follows.

1,0,2,0,3,0

A quadratic polynomial is of the form as follows.

fx=Ax2+Bx+C

Corresponding matrix equation is PX = Q.

Substitute the points in the quadratic polynomial as follows.

27=A02+B0+C0=A12+B1+C0=A22+B2+C0=A32+B3+C

Rewriting these equation as follows.

P=001111421931,X=ABC,Q=27000

According to the rule of least square solving PTPx=PTQas follows.

983614361461464ABC=27000

The solution is as follows.

A=6.75,B=28.35,C=25.35

So, the quadratic equation is as follows.

role="math" localid="1659689247907" f(x)=6.75x2-28.35x+25.35

The graph for the quadratic function is as follows.

Hence, the solution for the quadratic function is f(x)=6.75x2-28.35x+25.35.

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Most popular questions from this chapter

If then脳nmatrices Aand Bare orthogonal, which of the matrices in Exercise 5 through 11 must be orthogonal as well?AB.

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Consider a linear transformationL from RmtoRn that preserves length. What can you say about the kernel of L? What is the dimension of the image? What can you say about the relationship between n and m? If Ais the matrix of L, What can you say about the columns of A? What isATA? What aboutAAT? Illustrate your answer with an example where m=2and n=3.
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