Quadratic Functions

THE STANDARD FORM:   ax² + bx + cy² + dy + e= 0


**You need to know the equation above to be able to tell if a graph will be an ellipse, a circle, a hyperbola, or a parabola..


*If A does not equal C and the signs are the same, then the graph is an ellipse.



*If A and C are equal, then the equation is a circle.


*If A and C are different signs then the graph is a hyperbola.



*If A and C equal 0, then the graph is a parabola.

Graphing Absolute Value Equations

**Using this Equation: y = a l x - h l +k

*Using (h, k) will help you find the vertex of the graph.

*Using the a in the equation will determine if the graph will open up or down.

*The h will tell you if it will go left or right and the k will tell you if it moves up or down

Error Analysis

Problem number 22 is wrong because the line is supposed to be dotted not solid. The shaded part is right. In problem number 23 it's wrong because the shaded part is supposed to be above the line not under. The solid line is right in this problem.





This problem is wrong because the x is going up by 5's and the y's are going up by 10's so the equation is wrong. The slope should be 2 or 10/5. Putting these numbers in the equation should be correct.




When you solve these equations you always have to plug in the numbers into each equation to make sure that the answer is corect. If you just plug it into one equation it may be right for that equation but not the other.



Number 20 is wrong because the equation says less than which means that the line is supposed to dotted not solid.


In problem 21 the equation says that y is less than or equal to. The shaded area should be underneath the line not above.