Analyze the polynomial function $$ f(x)=x^{2}(x-8)(x+8) $$ using parts (a) through (e). (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The least zero is a zero of multiplicity $$ \square $$ so the graph of f . The greatest zero is a zero of multiplicity $$ \square $$, so the graph of f the x -axis at $$ \mathrm{x}=\square $$. The middle zero is a zero of multiplicity $$ \square $$, so the graph of $$ \mathrm{f} \square $$ the x -axis at $$ \mathrm{x}=\square $$. (d) Determine the maximum number of latning points on the graph of the function. $$ \square $$ (Type a whole number.) (e) Use the above information to draw a complete graph of the function. Choose the correct graph below.

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(a) The least zero is a zero of multiplicity 1, so the graph of f crosses the x-axis at x = -8. (b) The greatest zero is a zero of multiplicity 1, so the graph of f crosses the x-axis at x = 8. (c) The middle zero is a zero of multiplicity 2, so the graph of f touches the x-axis at x = 0 and then crosses it. (d) The maximum number of latning points on the graph of the function is 3. (e) The correct graph is the one that matches the characteristics: crosses at x = -8 and x = 8, touches and crosses at x = 0, and has 3 latning points.

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