The equation of the polyomial is f(x) = -(x + 1)^2(x -4)^2, and the y-intercept is -16
<h3>Find the zeros from the graph and their multiplicities, </h3>
The zeros of a graph are the points where the graph crosses or touches th x-axis
If the graph crosses the x-axis at a point, then the multiplicity at the point is 1.
However, if the graph touches the x-axis at a point, then the multiplicity at the point is 2.
Using the above as a guide, we have
Zeros = -1, Multiplicity = 2
Zeros = 4, Multiplicity = 2
<h3>Write an equation that could be the equation of this function. </h3>
In (A), we have
Zeros = -1, Multiplicity = 2
Zeros = 4, Multiplicity = 2
The equation is represented as
f(x) = -(x - zero)^muliplicity
So, we have
f(x) = -(x + 1)^2(x -4)^2
<h3>Use your equation to find the
y-intercept</h3>
In (b), we have
f(x) = -(x + 1)^2(x -4)^2
Set x to 0
So, we have
f(x) = -(0 + 1)^2 * (0 -4)^2
Evaluate
f(0) = -16
Hence, the y-intercept is -16
Read more about polynomials at
brainly.com/question/14506506
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