Question 1162056
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The quadratic function  Y = {{{(x-5)^2}}} is the parabola.


It has the axis of symmetry x= 5 (vertical line).


The line Y = k is a horizontal line.


The fact that the distance between the intersection  points is 10, means that these points are remoted 5 units 

in both directions from the symmetry axis x= 5.



It, in turns, means that the intersection points are at  x= 0  and  x= 10.


By substituting x= 0 into the quadratic funcrion, you get  Y = {{{(0-5)^2}}} = {{{5^2}}} = 25.


So, the answer is  k = Y = 25.


You will get the same answer, if you substitute  x= 10  instead of  x= 0 into the quadratic function.
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Solved and explained.