Question

1. The curve y = (x - 1)(x – 5) cuts the x-axis at A and B and the y-axis at C.

(a) Find the coordinates of A and B.
(b) Hence, find the coordinates of the turning point, M.
Is M a maximum or a minimum point?
(c) Find the coordinates of C.
(d) Sketch the graph of y = (x - 1)(x - 5).

Answer 1

So the first two questions are asking for points of intercept. a is asking where the function crosses the x, in this case it is where y=0. So your x intercept is at x= 1,5. Then to find the y intercept it is where x=0, so just substitute 0 for x. Then you get your y intercept as y=5. Because your coefficient for the quadratic function is positive your function has a minimum since it opens upward. I’m not sure what is means by C coordinate, but your vertex is at (3,-4) and lime of symmetry is at x=3.

X intercepts: (1,0) and (5,0)
Y intercept: (0,5)