Thus the -coordinate of the vertex is given by the expression

The -coordinate can be obtained by substituting the above result into the given quadratic equation, giving

As a practical matter, Vieta's formulas provide a useful method for finding the roots of a quadratic in the case where one root is much smaller than the other. If , then , and we have the estimate:

The second Vieta's formula then provides:

These formulas are much easier to evaluate than the quadratic formula under the condition of one large and one small root, because the quadratic formula evaluates the small root as the difference of two very nearly equal numbers (the case of large ), which causes round-off error in a numerical evaluation. Figure 5 shows the difference between (i) a direct evaluation using theGauchos Kick it Into Gear at Santa Clara Invitational

Photo by Francis Lipinski

Oct 18, 2013

The UC Santa Barbara cross-country teams return to action this Saturday, participating in the Santa Clara Bronco Invitational at Baylands Park in Sunnyvale, California. The race comes two weeks after the Gaucho men and women finished 3rd and 7th respectively in the NCAA West Regional Preview in Sacramento.

Dani Moreno and Christine Cooperstein have led the women's side this season, with Maxine Goyette providing quality performances as well. Saturday will be the 2nd time this season that the women have run a 6K race, taking part in their only other at the Riverside Invitational.

The men's team has provided great team efforts from top to bottom regularly, with the trio ofAnthony Ortolan, Bryce Rausa, and Andrew Farkas