Answer :
To find the vertex of the function [tex]\( f(x) = |x - 3| + 6 \)[/tex], we should consider the properties of the absolute value function in its vertex form.
The general form of an absolute value function is [tex]\( f(x) = |x - a| + b \)[/tex], where [tex]\((a, b)\)[/tex] is the vertex of the graph.
In the given function [tex]\( f(x) = |x - 3| + 6 \)[/tex], we can identify the following:
- The term inside the absolute value, [tex]\( x - 3 \)[/tex], indicates a horizontal shift of 3 units to the right from the origin.
- The constant term outside the absolute value, [tex]\( +6 \)[/tex], indicates a vertical shift of 6 units upwards.
Therefore, the vertex of the graph of the function [tex]\( f(x) = |x - 3| + 6 \)[/tex] is at the point [tex]\((3, 6)\)[/tex].
So, the vertex is located at [tex]\((3, 6)\)[/tex].
The general form of an absolute value function is [tex]\( f(x) = |x - a| + b \)[/tex], where [tex]\((a, b)\)[/tex] is the vertex of the graph.
In the given function [tex]\( f(x) = |x - 3| + 6 \)[/tex], we can identify the following:
- The term inside the absolute value, [tex]\( x - 3 \)[/tex], indicates a horizontal shift of 3 units to the right from the origin.
- The constant term outside the absolute value, [tex]\( +6 \)[/tex], indicates a vertical shift of 6 units upwards.
Therefore, the vertex of the graph of the function [tex]\( f(x) = |x - 3| + 6 \)[/tex] is at the point [tex]\((3, 6)\)[/tex].
So, the vertex is located at [tex]\((3, 6)\)[/tex].
