Math Problem Statement

For 𝑓(π‘₯) = (π‘₯ + 2)2(π‘₯ βˆ’ 1)(π‘₯ βˆ’ 2), answer the following. a) Show the leading coefficient and state the end behavior of the graph. You may use arrows. Leading Coefficient ___________ End Behavior ______________ b) Find the x-intercepts and their multiplicity and state whether the graph crosses or turns at that intercept. Intercept: _____________ Multiplicity: ___________ Cross or Touch: ___________ Intercept: _____________ Multiplicity: ___________ Cross or Touch: ___________ Intercept: _____________ Multiplicity: ___________ Cross or Touch: ___________ c) Find the y-intercept.

Solution

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Math Problem Analysis

Mathematical Concepts

Polynomial Functions
Intercepts
Graph Behavior
End Behavior

Formulas

General form of a polynomial: f(x) = a_n * x^n + a_(n-1) * x^(n-1) + ... + a_0
x-intercepts: Set f(x) = 0 and solve
y-intercept: Set x = 0 in f(x)

Theorems

Multiplicity affects whether a graph crosses or touches the x-axis
End behavior depends on the degree and leading coefficient of the polynomial

Suitable Grade Level

Grades 10-12