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solve for a and find ewuation of fx in factored firm

To solve for \( a \) and find the equation of \( f(x) \) in factored form based on the provided graph, we'll start by analyzing key features of the graph:

1. **Turning Points and Roots**:
   - The graph appears to be a polynomial with three turning points, indicating it might be of degree 4.
   - The roots of the polynomial (where the graph crosses the x-axis) are at \( x = 0 \) and \( x \approx 4.5 \).

2. **End Behavior**:
   - The left end of the graph approaches infinity as \( x \) decreases, and the right end approaches infinity as \( x \) increases. This end behavior is typical for even-degree polynomials with a positive leading coefficient.

Given this, the polynomial can be tentatively represented as:
\[
f(x) = a(x)(x - 4.5)
\]
where \( a \) is the leading coefficient, and we have a root at \( x = 4.5 \). Since it crosses the x-axis at \( x = 0 \), one factor must also be \( x \), and

Solve for 'a' and find the equation of f(x) in factored form.

Learn how to solve for the coefficient 'a' in a polynomial equation by analyzing roots and end behavior from a graph. This problem is ideal for high school students covering polynomial equations.

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