Hey surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 150 feet from a Pi
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First, we are going to find the vertex of our quadratic. Remember that to find the vertex 
of a quadratic equation of the form 
, we use the vertex formula 
, and then, we evaluate our equation at 
to find 
.
We now from our quadratic that
and 
, so lets use our formula:
Now we can evaluate our quadratic at 8 to find:
So the vertex of our function is (8,-72)
Next, we are going to use the vertex to rewrite our quadratic equation:
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.
We can conclude that:
The rewritten equation is
The x-coordinate of the minimum is 8
We now from our quadratic that
Now we can evaluate our quadratic at 8 to find
So the vertex of our function is (8,-72)
Next, we are going to use the vertex to rewrite our quadratic equation:
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.
We can conclude that:
The rewritten equation is
The x-coordinate of the minimum is 8