a) Coordinates of A (1, 0), Coordinates of B (3, 0).
b) Coordinates of P (0, 3).
c) Coordinates of Q (2, -1).
Step-by-step explanation:
Step 1; The equation of the plot is y = (x -1)(x -3). So to find the values of A and B we substitute y = 0 as A and B are on the x axis which means the value of y = 0.
So x -1 = 0, x -3 = 0, So x = 1 and x = 3.
So A = (1, 0) and B = (3, 0).
Step 2; To solve for P, we substitute x = 0 as the point P is on the y axis where the value of x equals 0. So when y = (x -1)(x -3) and x = 0, the equation becomes
y = (0 -1)(0 -3) = (-1)(-3) = 3.
So the coordinate of P is (0, 3).
Step 3; The x value of the vertex of any parabola i.e. the lowest or highest point depending on the type of parabola is given by [tex]\frac{-b}{2a}[/tex]. We subtitute this value of x in y to determine the value of y.
y = (x -1)(x -3) = x² - 4x + 3. Here a = 1, b = -4 and c = 3.
x = [tex]\frac{-b}{2a}[/tex] = [tex]\frac{-(-4)}{2(1)}[/tex] = [tex]\frac{4}{2}[/tex] = 2.
Substituting x =2 in y, we get
y = (2 -1)(2 -3) = (1)(-1) = -1.
So the coordinate of Q is (2, -1)
