Algebra 2 Test Review

1. Algebra 2 Test Review Kristin Collins

2. Introduction • Conic Secrions

3. Topics of Discussion • Parabolas , Ellipses , Circles and Hyperbolas

4. Parabolas • The two standard forms of parabolas • y=a( x – h)^2 +k • X=a( y – k )^2 +h • For the first form , the parabola will either open up or down depending on whether a is positive or negative. • For the second form , the parabola will open to the left or right depending on whether a is positive or negative. • This information relates to the class because they are preparing for a test.

5. Ellipse • The standard equation for an ellipse is x^2/a^2 +y^2/b^2 =1 • The a and b in the standard equation stand for the major and minor axis. Also , (a,0) and (-a,0) are the major intercepts. Also , (0,b) and (0,-b) are the minor intercepts where a^2 is greater than b^2. c^2 =a^2-b^2 and (c,0) and • (-c,0) are the foci of the ellipse.

6. Circles c The standard formula of a circle centered at (h , k ) is (x-h)^2 + ( y – k) ^2 = r^2 Where r is the radius.

7. Hyperbolas The equation of a hyperbola is X^2/a^2-y^2/b^2 =1 Where (a,0) and (-a,0) are the vertices And (c,0) and (-c,0) are the foci. C^2=a^2+b^2

8. What This Means • Circle is the set of points in a plane that are equidistant from one point, the center • Parabolas are the set of points in a plane that are the same distance from a given point and a given line in the plane. • Ellipse is the set of points in a plane such that sum of distances from two given points in that plane stays constanc • Hyperbola is the set of all points in a plane such that the absolute value of the difference of the distances between two given points stays contant.

9. Next Steps • Try some example by replacing the variable with numbers and then graphing them. • Then try to visualize the graph without graphing it. • Think of some real life examples of these conic sections. For example, the reflector in a flashlight.