Generalize Exercise 87: Show that if the horizontal line y = c intersects the graph of (x)

Generalize Exercise 87: Show that if the horizontal line y = c intersects the graph of ƒ(x) = x² + rx + s at two points

Figure 26

Data From Exercise 87

Show that if the quadratic polynomial ƒ(x) = x² + rx + s takes on both positive and negative values, then its minimum value occurs at the midpoint between the two roots.

Transcribed Image Text:

x1 + x2 (x₁, f(x1)) and (x2, f(x2)), then f takes its minimum value at the midpoint M = 2 (Figure 26).