Chapter 5 Polynomials and Polynomial Functions - 5.9 Write Polynomial Functions and Models - 5.9 Exercises - Quiz for Lessons 5.7-5.9 - Page 399: 10

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Given: $f(x)=(x-3)(x+2)^2(x+3)^2=(x-3)(x+2)(x+2)(x+3)(x+3)$ Find x-intercepts: $x-3=0 \rightarrow x=3\\x+2=0\rightarrow x=-2\\x+3=0\rightarrow x=-3$ Let's find some points: $x=-5 \rightarrow y=-288\\x=-1\rightarrow y=-16\\ x=1\rightarrow y=-288 \\x=4 \rightarrow y=1764$ $f(x) \rightarrow -\infty$ as $x \rightarrow -\infty$ $f(x) \rightarrow \infty $ as $x \rightarrow \infty$