Step-by-step explanation:
The value of k in the equation g(x) = f(x) + k comes out to be 8.
How the vertical shifting of a graph takes place?
If the graph of a function f(x) is shifted vertically by k units, f(x) becomes f(x)+k.
From the diagram, we can say that graph of f(x) has been shifted vertically by 8 units
If we shift f(x) vertically by 8 units f(x) becomes f(x)+8 and also coincides with the graph of g(x).
So, g(x) = f(x) + 8........(1)
Comparing (1) and g(x) = f(x) + k, we get k=8.
Hence, the value of k in the equation g(x) = f(x) + k comes out to be 8.
The answer is x= -2 hope this helps!
The vertex is the minimum or the maximum point of the parabola.
<em>x and f(x) represent the horizontal and the vertical coordinates of the vertex.</em>
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The standard form of a parabola is

The x coordinate of the parabola is calculated using:

The value of the x-coordinate is then plugged in, into the equation to calculate the y-coordinate, as follows:

At the end of the calculation,
x and f(x) represent the horizontal and the vertical coordinates of the vertex.
Take for instance:

The x-coordinate of the vertex is:




The y-coordinate is:



So, the vertex of
is (-1,11)
See attachment for illustration of vertex of 
Read more about vertex of parabola at:
brainly.com/question/20209326
The answer is the fourth one
Answer:
64.5°
Step-by-step explanation:
angle of elevation is the angle from the point where the shadow ends. this create a right angle triangle. using tan, you can find the angle.
tan theta = opposite/adjacent
angle = tan^-1(42/20)
angle = 64.5°