| Quad means square in Latin. A quadratic equation is polynomial where the highest order term is a square; it is thus said to be a second order polynomial. Quadratic equations are very important for two reasons: 1) They can represent a wide variety of things like motion in the real world, and 2) We can find solutions for them. While there is a general formula for solving quadratic equations, it requires a good deal of calculation and taking square roots. Therefore, we look for tricks, special cases that are easier to solve. |
 |
15.1 Solving Quadratic Equations |
- Solve quadratic equations by factoring.
- Set quadratics equal to zero.
- Solve quadratics by taking the square root of both sides of the equation.
- Determine if a solution is a real or complex number. |
|
|
|
15.2 Solving by Completing the Square |
- Recognize the perfect square pattern for trinomials.
- Factor perfect square trinomials.
- Complete the square on a trinomial.
- Solve quadratic equations by completing the square. |
|
|
|
|
15.3 Graphing Quadratic Equations |
- Know how the constants a, b, and c change the shape of a parabola.
- Determine equation for the axis of symmetry of the parabola.
- Find the real roots of a parabola from the equation.
- Find the vertex of a parabola from the formula. |
|
|
|
|
15.4 The Quadratic Formula |
- Solves quadratic equations using the quadratic formula.
- Applies the discriminant to determine the number of real and complex roots. |
|
|
15.5 Additional Assignments |
- Applies knowledge of parabolas to motion problems.
- Visualizes complex roots graphically. |
|
|
|
|
