What is the simplest form of polynomial used to approximate a function?

Understanding Polynomial Approximation

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard

Sophia Harris
FREE Resource
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5 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A cubic polynomial
A constant
A quadratic polynomial
A linear polynomial
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can the approximation of a function be improved beyond a constant?
By adding a quadratic term
By matching the first derivative at a point
By using a cubic polynomial
By increasing the constant value
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What additional term is added to create a quadratic approximation?
A linear term
An x cubed term
A constant term
An x squared term
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the 1/2 factor used in the quadratic term of the approximation?
To adjust the constant term
To make the polynomial a power series
To ensure the second derivative matches
To simplify the polynomial
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of matching higher-order derivatives in polynomial approximation?
To improve the approximation accuracy
To reduce the number of terms
To make the polynomial more complex
To simplify the calculation
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