AM 3 Lesson 3:

1. AM 3 Lesson 3: Ellipses and Intro to Parabolas (not what you think  )

2. From the warm up…. • Find the rule for the bottom half of the ellipse • Solve for y, chose bottom half • Use graphing calculator to show intersection between line and ellipse (compare with #8 on WU) • Set y=0 to show no real zero exists.

3. Completing the Square (CTS) • Given: • Use Completing the square to rewrite in vertex form • Some of the usefulness of CTS is to rewrite equations in ellipse or circle equation form in order to help us graph. • Example: Rewrite in ellipse form. • Use CTS to rewrite • Identify the center, radius, diameter, sketch the graph • Domain/Range? • Practice: • (Start here)

4. CFU Answers (complete practice prev page) • 6) 7)

5. Intro to Parabolas • Some parabolas are concave up or down • These are parabolas which exist as functions • Some parabolas are concave right or left • These parabolas are not functions, they are relations • The equation of a parabola of this nature is: • The vertex is (h,k). (h and k are both opposite) • If a>0 the parabola is concave right • If a<0 the parabola is concave left

6. Example: • Graph: • Identify the vertex, concavity, domain and range, and axis of symmetry • Label the vertex and identify the max/min • Label two points on the graph (look at concavity and choose the next closest x-value and find the two corresponding y values)

7. Graph: • List at least one point on the top and bottom • Plug in x=2 and find the 2 corresponding y values.

8. Answer with steps…..