write the coordinates of the vertex of the parabola Y= (x-5)^2

Question

this is a parabola question from grade 10 mathematics chapter 4 lesson 5 im having troublle with id be glad for any help thank yyouu

Answer 1

The vertex is located at (5,0).  All perfect squares (e.g., (x-5)²) have their vertex on the x-axis.  The graph of y=x² is located at the origin, (0,0).  Using function transformations, (x-5)² is shifted 5 units to the right from the origin to (5,0).

 

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Another way to find out is to note that the equation is in the vertex form:

 

y-k = (x-h)²

 

where (h,k) are the coordinates of the vertex.  In this case, h = 5 and k = 0.  Hence the vertex is located at (5,0).