The polynomial function \( g \) is graphed at right. Give an **equation** of the polynomial. To find the leading coefficient, use the fact that the graph goes through the point \( (1, 20) \).**Graph Explanation**The graph represents the function \( y = g(x) \) and is plotted on a Cartesian plane with the x-axis and y-axis. Key Features:- The curve has several turning points, suggesting it is a polynomial of higher degree.- The curve descends steeply around \( x = -8 \), goes below the x-axis, reaches a minimum at \( x = -6 \), and then increases, crossing the x-axis at \( x = -4 \).- It again dips and rises, creating another turning point between \( x = -2 \) and \( x = 3 \).- The curve goes through the point \( (1, 20) \), which is essential for determining the leading coefficient.- Beyond \( x = 3 \), the graph sharply increases.

To give an equation of the polynomial whose graph is given below.The graph passes through the point .From the graph of the polynomial function ,we observe that, the graph touches the -axis and bounces back at .So, is a zero of multiplicity 2 (even multiplicity). Since, the graph passes through the -axis but flattens out a bit first at So, is a zero of multiplicity 3 (odd multiplicity). Since, the graph touches the -axis and bounces back at .So, is a zero of multiplicity 2 (even multiplicity). Therefore, the zeros of the polynomial function are given by Let the leading coefficient of the polynomial is .Now, the equation of the polynomial function is given by Since, the graph of the polynomial is passing through the point .Substituting, , in (1), we getSubstitiuting, , in (1), we getHence, the equation of the polynomial is .Answer: