review Guide for alg II HP on quadratics

The test next Friday 10/20 for quadratics should have around 10 problems on it.

Main concepts

being able to find the vertex of a function using algebra (-b/2a)

being able to graph using vertex or standard form
be able to solve any quadratic (R or i  solutions)
be able to write a quadratic given solutions and another point (like y-int.)
be able to write a quad equation from points that are not solutions
be able to do operations with i, including rationalizing the denominator
be able to solve a non-linear system
be able to set up an equation and solve a quad application problem


Here are a few sample problems

1. Write the function for a quadratic with x-intercepts at (6, 0) and (-2, 0) and has a y-int = 3

1. Write the function for a quadratic with the vertex at (-4, 5) containing the point (2, -11).
2. Write an equation that has solutions x = 1/2, 5
3. write a quad function that has solutions x = 2 + 4i, 2 - 4i
4.     (5, -3), (6, 3) and (1, 13) are points on a parabola.  Write the function that would include these points
5. solve:  x^2 = -8x -15
6. solve:  y =  2x^2 +19x + 24
7. solve:  x^2 -10x = 11
8. How high does a ball go up if its path is modeled by h(x) = -16x^2 + 160x   where x is horizontal distance and h is height.
9.  Check out some of the elimination problems in section 3.5 solving non linear systems
10. 10. simplify  (3+i) / (i-9)
11.   You have 1,000 feet of fencing to make 2 pens to hold animals.  What is the maximum area you can make from this amount of fencing.