Write polynomial functions from solutions of that polynomial function.
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In terms of pacing, this lesson can be taught over two days.
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Sarah is given two points that lie on a line.
$${f(8)=0 }$$
$${f(-2)=5}$$
She first writes the slope intercept form of the equation:
$${y=mx+b}$$
Then, she substitutes one point into the equation:
$${0=(8)m+b}$$
She then substitutes the other point into the slope intercept form:
$${5=(-2)m+b }$$
What are Sarah’s next steps in finding the equation of this line?
Algebra II > Module 1 > Topic B > Lesson 20 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
The general form for a polynomial function is:
$${{a_n}x^n+a_{n-1}x^{n-1}+a_1x+a_0 ...}$$
where $$n$$ is the degree of the polynomial, and $$a_{n}$$ is the leading coefficient.
So, for example: a 4th-degree polynomial has a general form of:
$${ax^4+bx^3+cx^2+dx+e}$$
What is the largest degree you could uniquely define if you were given three points?
What is the polynomial $$P$$ such that $$P(-1)=10$$, $$P(2)=1$$, and $$P(0)=3$$?
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Use the remainder theorem to find a quadratic polynomial $$P$$ so that $$P(1)=5$$, $$P(2)=12$$, and $$P(3)=25$$. Give your answer in standard form.
Algebra II > Module 1 > Topic B > Lesson 20 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..