The roots here are easily seen as x= 1 or x= 2. That means r= 1 and s= 2. Because the parabola opens
upward, we should look for an absolute minimum. Its x-value is
xmin= (r+s)/2
= (1 + 2)/2
= 3/2
To find the y-value, we plug 3/2 into the quadratic function and grind out the arithmetic:
y= (3/2)^2 − 3 × 3/2 + 2
= 9/4 − 9/2 + 2
= 9/4 − 18/4 + 8/4
= (9 − 18 + 8) / 4
=−1/4
Now we know that the coordinates of the absolute minimum are (3/2, −1/4). We also know that the points
(1, 0) and (2, 0) lie on the parabola. Figure 24-4 shows these points. They’re close together, so it’s difficult
Figure 24-4 Approximate graph of y=x^2 − 3 x+ 2,
where the independent variable is x and the
dependent variable is y. On both axes, each
increment represents 1/4 unit.
x
y
(0,2)
(1,0)
(2,0)
(3/2,–1/4)
Each axis increment
is 1/4 unit
Two Real Zeros 401