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put this solution on YOUR website!First thing to notice is that two of the points are on the x-axis and that tells us that we have a parabola whose axis is perpendicular to the x-axis, i.e. vertical, and that the x-coordinates of these two points are the zeros of the desired polynomial function.
Knowing that we have two zeros for a 2nd degree polynomial, we can derive A quadratic function simply by multiplying
. However, this misses the mark because if you calculate the y-intercept you get (0,-12) instead of the desired (0,2).
Fortunately, you can multiply any polynomial by any constant and not change the zeros.
,
, and
all have the same zeros, namely 1 and -5.
So for the function in question, we need to answer, "What can we multiply by so that the constant term will be 2?" Answer:
.
So:
is the desired function.
Check:
