With L` Hospital`s Rule ( ( tan x ) ` = 1/ cos^2 x ) :
What is the vertex of the graph of f(x) = |x – 13| + 11?
2 answers:
Answer:
The vertex of the graph of f(x) = |x - 13| + 11 is (13, 11).
Step-by-step explanation:
There is something called absolute value in the given function. It means two equations will result from it.
When the resultant equation is
- This will be the first equation
or
When the resultant equation is
- This will be the second equation.
The intersection of these lines will give the vertex as found by solving both equations at the same time.
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Replacing the value of for any one;
(first one)
(second one)
The vertex is (13, 11)
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Answer:
- square: 9 square units
- triangle: 24 square units
Step-by-step explanation:
Using a suitable formula the area of a polygon can be computed from the coordinates of its vertices. You want the areas of the given square and triangle.
<h3>Square</h3>The spreadsheet in the first attachment uses a formula for the area based on the given vertices. It computes half the absolute value of the sum of products of the x-coordinate and the difference of y-coordinates of the next and previous points going around the figure.
For this figure, going to that trouble isn't needed, as a graph quickly reveals the figure to be a 3×3 square.
The area of the square is 9 square units.
<h3>Triangle</h3>The same formula can be applied to the coordinates of the vertices of a triangle. The spreadsheet in the second attachment calculates the area of the 8×6 triangle.
The area of the triangle is 24 square units.
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<em>Additional comment</em>
We have called the triangle an "8×6 triangle." The intention here is to note that it has a base of 8 units and a height of 6 units. Its area is half that of a rectangle with the same dimensions. These dimensions are readily observed in the graph of the vertices.
