Answer:
a)
A (1, 0)
B (3,0)
b)
P(0,3)
c)
Q(2, -1)
Explanation:
The equation (x-1)(x-2) is a quadratic equation and represents the equation of a parabola
Part a)
The x-intercepts at A and B represent the zeros of the function
Set (x-1)(x-3) = 0 ===> x = 1 and x =3
So the x-intercepts which are the x values at y = 0 are
A(1, 0) and B(3,0)
Part b
P is the y intercept and can be obtained by setting x = 0 and solving for y
==> y = (0-1)(0-3) = -1 x -3 = 3
So P(0, 3)
Part c
Q is the vertex of the parabola and represents a minimum point for the graph
The minimum value for x can be found by differentiation the function with respect to x and setting it equal to 0 and solving for x value
We have y = (x-1)(x-3) = x² -1x - 3x + 3 using the FOIL method
y = x² - 4x + 3
dy/dx = 2x -4
Setting dy/dx = 0
==> 2x - 4 = 0
x2x = 4
x = 2
So the minimum occurs when x = 2
At x = 2,
y = (2-1)(2-3) = 1 x -1 = -1
So the vertex is at (2, -1) which is point Q