Answer:
A(1, 0), B(3, 0), P(0, 3), Q(2, -1)
Step-by-step explanation:
Points A and B are the x-intercepts of the graph. The values of x at those points are values that make the value of y be zero. The zero product rule tells you these must be the values that make the factors of y = 0.
x -1 = 0 ⇒ x = 1
x -3 = 0 ⇒ x = 3
This means ...
A = (1, 0)
B = (3, 0)
__
The value of y at the y-intercept is the value when x=0:
y = (0 -1)(0 -3) = 3
P = (0, 3)
__
The x-coordinate of the vertex is on the line of symmetry, halfway between the x-intercepts.
Qx = (1 +3)/2 = 2
The y-coordinate of the vertex is the value of y for that value of x.
y = (2 -1)(2 -3) = (1)(-1) = -1
The coordinates of Q are ...
Q = (2, -1)
_____
Additional comment
A graphing calculator can help you with questions like this.
