Solving Applications Modeled By Quadratic Equations Summary

Key Concepts

• Area of a Triangle For a triangle with base, \(b\), and height, \(h\), the area, \(A\), is given by the formula: \(A=\frac{1}{2}bh\)
  
• Pythagorean Theorem In any right triangle, where \(a\) and \(b\) are the lengths of the legs, and \(c\) is the length of the hypothenuse, \({a}^{2}+{b}^{2}={c}^{2}\)
  
• Projectile motion The height in feet, \(h\), of an object shot upwards into the air with initial velocity, \({v}_{0}\), after \(t\) seconds can be modeled by the formula:
  \(h=-16{t}^{2}+{v}_{0}t\)

Glossary

consecutive even integers

Consecutive even integers are even integers that follow right after one another. If an even integer is represented by \(n\), the next consecutive even integer is \(n+2\), and the next after that is \(n+4\).

consecutive odd integers

Consecutive odd integers are odd integers that follow right after one another. If an odd integer is represented by \(n\), the next consecutive odd integer is \(n+2\), and the next after that is \(n+4\).