F(x)=x^2-8x+12 in vertex form
1 answer:
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For a better understanding of the solution provided here please go through the diagram in the file that has been attached.
As can be clearly seen from the question and the graph, the area is bounded by a straight line which passes through the origin, the y axis and the horizontal line
.
As we can see from the graph, this is a right triangle. To find the point of intersection of the horizontal line y=6 and the line , we will have to equate the two as:
Therefore,
Thus,
Hence the point of intersection is (12,6) which is depicted on the graph too.
As this is a case of a simple right triangle, the area of the bounded region will thus be:
Let the base be the y=6 line whose length is 12 and let height be the y axis whose length is 6, thus, the area will be:
squared units.
The recursive formula
means that, to compute the next value, you have to double the previous one and then add 5.
So, we start with 5. To get the second term, we double it and add five, so we have
Next, we will double 15 and add 5:
So, the answer is B, because it's the only option starting with 5,15,35.
Just to check, let's compute the last step:
Which confirms option B