Final answer:
The axis of symmetry for the absolute value equation y = |x - 4| + 10 is the vertical line X = 4, which is the equation of the axis of symmetry.
Step-by-step explanation:
The correct answer is option X=4. This equation represents an absolute value function, which always has a vertex that serves as the point of symmetry. In the equation y = |x - 4| + 10, the vertex occurs where the expression inside the absolute value equals zero.
To find this point, we set x - 4 equal to zero, which gives us x = 4. Therefore, the axis of symmetry is the vertical line passing through the vertex, which can be described by the equation X = 4.
The correct answer is option X=4. To find the axis of symmetry of the absolute value equation y=|x-4|+10, we need to determine the value of x that makes the expression inside the absolute value equal to zero.
This is because when the expression inside the absolute value is zero, the whole equation will be zero, resulting in the minimum value of y. So, setting x-4=0, we find that x=4. Therefore, the axis of symmetry is the vertical line x=4.