Questions: Which equation choice could represent the graph shown below? Answer: f(x) = x(x - 3)(x + 7) f(x) = x(x + 3)(x - 7) f(x) = x(x - 3)(x - 7) f(x) = x(x + 3)(x + 7)

Which equation choice could represent the graph shown below? Answer: f(x) = x(x - 3)(x + 7) f(x) = x(x + 3)(x - 7) f(x) = x(x - 3)(x - 7) f(x) = x(x + 3)(x + 7)
Transcript text: Which equation choice could represent the graph shown below? Answer: $f(x) = x(x - 3)(x + 7)$ $f(x) = x(x + 3)(x - 7)$ $f(x) = x(x - 3)(x - 7)$ $f(x) = x(x + 3)(x + 7)$
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Solution

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Solution Steps

Step 1: Analyze the graph's x-intercepts

The graph intersects the x-axis at x = -7, x = 0, and x = 3. These are the roots of the equation.

Step 2: Determine the factors

Since the roots are -7, 0, and 3, the factors of the equation will be (x+7), x, and (x-3).

Step 3: Form the equation

The equation will be the product of the factors: f(x) = x(x+7)(x-3) or f(x) = x(x-3)(x+7).

Final Answer:

\\( \boxed{f(x) = x(x-3)(x+7)} \\)

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