Algebra Know-It-ALL

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