You should KNOW

1. That a quadratic funcion is one having the form

*f(x)=ax^2+bx +c* and that its graph is a parabola.

2. That you can complete the square to express a quadratic function as *f(x) = a(x-h)2 + k *where *(h,k)* are the coordinates of the vertex of the parabola which is the graph of f, the coefficient *a* tells us the direction and size in which the parabola opens, and the x-intercepts are the solutions of the corresponding quadratic equation.

3. How to use information about the graph to determine where f is increasing or decreasing, its range, and its mininum or maximum value.

4. That a quadtratic equation is an equation of the form

*ax2 +bx +c=0*

and that any such equation can be solved by completing the square or by using the quadratic formula.

5. The exact statement of the quadratic formula and how to apply it.

6. That there are specially invented numbers called __complex numbers__ that arise when the quadratic formula is used to solve quadratic equations that have no real solutions.

7. That quadratic equations may have 2, 1 or no real solutions, but that when there are no real solutions there will be two *complex *solutions.

8. How to factor quadratics when possible and how to use factoring to solve quadratic equations, recognizing that completing the square and the quadratic formula are usually more effective ways to solve these equations.

9. The special factorizations of a^2-b^2 and its variations.

10. How to solve quadratic inequalities by factoring or by the method of test points.

You should be ABLE TO

1. Determine the vertex of a parabola by completing the square.

2. Roughly sketch the graph of quadratic function without use of a graphing calculator, by determining its vertex, intercepts, direction of opening, and plotting selected points.

3. Solve quadratic equations, including those arising from word problems, showing all work and using a calculator only to do arithmetic.

4. Determine where a quadratic function is increasing/decreasing and any maximum or minimum values, without use of a calculator, and apply this to problems.