Unit 2, Lesson 6
Different Forms
Integrated Math 3
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Which three go together? Why do they go together?
A
B
C
D
We can make a box from a piece of paper that is 8.5 inches by 14 inches by cutting squares of side length from each corner and then folding up the sides. The volume , in cubic inches, of the box is a function of the side length , where .
Use the distributive property to show that each pair of expressions is equivalent.
Let and .
We can express polynomials in different, yet equivalent, algebraic forms that each give us different information about features of the polynomial and its graph. Earlier, we saw how expressing a polynomial function in factored form is helpful for identifying zeros. The expanded version of factored form, or standard form of a polynomial, is helpful for identifying the constant term and the degree.
For example, here are the expressions for a polynomial written in factored form and standard form:
The constant term, seen as -4.5 in the example, tells us the value of the function when . In a graph of the function, this point is known as the vertical intercept.
The degree, seen as 5 in the example, tells us about the general shape of the graph of the polynomial, which we’ll learn more about in future lessons.