For the function yx12x5 find its y intercept and its x inter

For the function y=(x-1)^2(x-5), find its y intercept and its x intercepts

Solution

We have y = (x - 1)² ( x - 5) .

The y -intercept is the point where x = 0,. On substituting x = 0 in the above equation, we get y = ( - 1)² ( - 5) = - 5. Thus, the y-intercept is - 5 . This means that the graph of the given function meets the Y -axis at the point ( 0, - 5)

The x -intercept is the point where y = 0,. On substituting y = 0 in the above equation, we get (x - 1)² ( x - 5) = 0. Then, either x - 1 = 0 which means that x = 1 or x - 5 = 0 which means that x = 5. Thus, there are two x -intercepts 1 and 5. The graph of the given function crosses the X -axis at the points ( 1 , 0 ) and ( 5 , 0).