Unit 2, Lesson 3

Introducing Polynomials

Algebra 2

Practice

Problem 1

Select all points where relative minimum values occur on this graph of a polynomial function.

<p>function graph with points on it. A, G, H on decreasing portions. C on increasing portion. relative minimums at B and E. relative maximums at D and F. </p>

Point \(A\)
Point \(B\)

Point \(C\)

Point \(D\)

Point \(E\)

Point \(F\)

Point \(G\)

Point \(H\)

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Problem 2

Add one term to the polynomial expression \(14x^{19}-9x^{15}+11x^4+5x^2+3\) to make it into a 22nd-degree polynomial.

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Problem 3

Identify the degree, leading coefficient, and constant value of each of the following polynomials:

\(f(x)=x^3 - 8 x^2 - x + 8\)
\(h(x)=2 x^4 + x^3 - 3 x^2 - x + 1\)
\(g(x)=13.2 x^3+3 x^4 - x - 4.4\)

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Problem 4

ForLesson 1: Let’s Make a Box

We want to make an open-top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard is a 9-inch by 9-inch square. The volume \(V(x)\), in cubic inches, of the open-top box is a function of the side length \(x\), in inches, of the square cutouts.

Write an expression for \(V(x)\).
What is the volume of the box when \(x=1\)?
What is a reasonable domain for \(V\) in this context?

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Problem 5

ForLesson 2: Funding the Future

Consider the polynomial function \(p\) given by \(p(x)=7x^3 - 2x^2 + 3x+10\). Evaluate the function at \(x=\text-3\).

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Problem 6

from an earlier course

Here is a graph that represents \(y = x^2\).

On the same coordinate plane, sketch and label the graph that represents each equation:

\(y = x^2 -8\)
\(y = \text-x^2 + 4\)

<p>A curve in an x y plane, origin O.</p>

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Introducing Polynomials

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Lesson 3 Resources