write the vertex form equation of each parabola.
1) Vertex:(-5,8), Focus:(-21/4, 8)
2) Vertex:(-6,-9), Directrix: x= 47/8
3)Vertex(8,-1) y- intercept: -17
4) Open left or right, Vertex: (7, 6), passes through:(-11,9)
5)Focus(-63/8, -7), Directrix: x= -65/8
6 Opens up or down, and passes through (−6, −7), (−11, −2), and (−8, 1)
7) Vertex at origin, opens left, 1/8units between the vertex and focus.
8) Vertex: (10, 0), axis of symmetry: y = 0,
length of latus rectum = 1, a < 0
4 answers
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To get you started, the parabola
y^2 = 4px has
vertex at (0,0)
focus at (0,p)
directrix is the line x = -p
latus rectum has length 4p
So, for
5)Focus(-63/8, -7), Directrix: x= -65/8
The distance between focus and directrix is 2p, so 2p = 1/4, p = 1/8
Since the directrix is a vertical line, the axis is horizontal
Since the focus is at y = -7, that is the axis
The vertex is at (-64/8,-7) = (-8,-7)
So the equation is
(y+7)^2 = 1/2 (x+8)
See the graph and properties at
https://www.wolframalpha.com/input/?i=parabola+%28y%2B7%29%5E2+%3D+1%2F2+%28x%2B8%29
To get you started, the parabola
y^2 = 4px has
vertex at (0,0)
focus at (0,p)
directrix is the line x = -p
latus rectum has length 4p
So, for
5)Focus(-63/8, -7), Directrix: x= -65/8
The distance between focus and directrix is 2p, so 2p = 1/4, p = 1/8
Since the directrix is a vertical line, the axis is horizontal
Since the focus is at y = -7, that is the axis
The vertex is at (-64/8,-7) = (-8,-7)
So the equation is
(y+7)^2 = 1/2 (x+8)
See the graph and properties at
https://www.wolframalpha.com/input/?i=parabola+%28y%2B7%29%5E2+%3D+1%2F2+%28x%2B8%29
1 answer