What is the equation, In factored form, of the quadratic function shown in the graph?

Given:

The graph of a quadratic function.

To find:

The equation of the quadratic function in factored form.

Solution:

From the given graph it is clear that the graph of the function intersect the x-axis at point (-3,0) and (2,0).

Since -3 and 2 are the zeros of the function, therefore (x+3) and (x-2) are the factors of the required quadratic function.

Now, the function can be written as:

            ...(i)

The graph of the function intersect the y-axis at (0,-6). Substituting in (i), we get

Substituting in (i), we get

Therefore, the required function is .

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