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# Alg2 lesson 8-2

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### Alg2 lesson 8-2

1. 1. Vertex form (standard form) for the equation of a parabola<br />y = a(x – h)2 + k<br />x = a(y – k)2 + h<br />Vertex: (h, k)<br />Vertex: (h, k)<br />Line of symmetry: x = h<br />Line of symmetry: y = k<br />
2. 2. Graph x = 2y2 + 8y + 9<br />x = (2y2 + 8y ) + 9<br />x = 2(y2 + 4y + 4) + 9 - 8<br />x = 2(y+ 2)2 + 1<br />Vertex: (1, -2)<br />Axis of symmetry: y = -2<br />Opens to the right<br />
3. 3. focus<br />latus rectum<br />directrix<br />All points on the parabola are equidistant from the focus and the directrix.<br />
4. 4. y = a(x – h)2 + k<br />focus<br />1 4a<br />same distance<br />directrix<br />
5. 5. y = a(x – h)2 + k<br />focus<br />latus rectum<br />1 a<br />length =<br />directrix<br />
6. 6. Pg 422<br />
7. 7. 4(y – 2) = (x + 3)2<br />4y – 8 = (x + 3)2<br />4y = (x + 3)2 + 8<br /> 4 4<br />y = ¼ (x + 3)2 + 2<br />a = ¼ <br />h = -3<br />k = 2<br />y = a(x – h)2 + k<br />
8. 8. y = ¼ (x + 3)2 + 2<br />vertex: (-3, 2)<br />axis of symmetry: x = -3<br />a = ¼<br />distance from vertexto focus = = 1 <br />distance from vertexto directrix = 1<br /> 1_4(¼)<br />Length of latus rectum:<br />1 = 4 units¼ <br />
9. 9. 4x – 13 = y2 – 2y <br />4x – 13 = (y2 – 2y ) <br />4x = (y – 1)2 + 12<br /> 4 4<br />x = ¼ (y – 1)2 + 3<br />x = a(y – k)2 + h<br />+1 – 1 <br />+13 +13 <br />
10. 10. x = ¼ (y – 1)2 + 3<br />vertex: (3, 1)<br />axis of symmetry: y = 1<br />a = ¼<br />distance from vertexto focus = = 1 <br />distance from vertexto directrix = 1<br /> 1_4(¼)<br />Length of latus rectum:<br />1 = 4 units¼ <br />