Illustrative Mathematics - Geometry - Unit 6 - Lesson 8

Write an equation that states (x,y) is the same distance from (4,1) as it is from the x-axis.

Tags

A.SSE.3.a

A.SSE.3.b

G.GPE.2

A.SSE.3.c

Select all equations which describe the parabola with focus (-1,-7) and directrix y=3

• {"blocks":[{"key":"0","text":"(x-1)^{2}+(y-7)^{2}=(y+3)^{2}","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":29,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"(x+1)^{2}+(y+7)^{2}=(y-3)^{2}","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":29,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"y=-20(x+1)^{2}-2","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":16,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"y=-\\frac{1}{20}(x+1)^{2}-2","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":26,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"y=-\\frac{1}{20}(x+1)^{2}+2","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":26,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}

Tags

A.SSE.3.a

A.SSE.3.b

G.GPE.2

A.SSE.3.c

Parabola A and parabola B both have the x-axis as the directrix. Parabola A has its focus at (3,2) and parabola B has its focus at (5,4). Select all true statements.

• Parabola A is wider than parabola B.
• Parabola B is wider than parabola A.
• The parabolas have the same line of symmetry.
• The line of symmetry of parabola A is to the right of that of parabola B.
• The line of symmetry of parabola B is to the right of that of parabola A.

Tags

A.SSE.3.a

A.SSE.3.b

G.GPE.2

A.SSE.3.c

A parabola has focus (5,1) and directrix y=-3. Where is the parabola’s vertex?

Tags

A.SSE.3.a

A.SSE.3.b

G.GPE.2

A.SSE.3.c

Suppose this two-dimensional figure is rotated 360 degrees using the vertical axis shown. Each small square on the grid represents 1 square inch. What is the volume of the three-dimensional figure?

Tags

A.SSE.3.a

A.SSE.3.b

G.GPE.2

A.SSE.3.c