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Find the coordinates of the vertex, focus, and endpoints of the lactus rectum. Also, find the equation of the directrix. Then sketch the graph of the parabola.

x^2 = -7/2 y

2
by djdelacruz19

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x^2 = -7/2 y

by djdelacruz19

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Vertex = (0,0)

focus = (0,-7/8)

latus rectum =(-7/4,-7/8) and (7/4,-7/8)

directrix ; y=7/8.

focus = (0,-7/8)

latus rectum =(-7/4,-7/8) and (7/4,-7/8)

directrix ; y=7/8.

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X²=-7/2y

If the x is squared, then it opens either upward or downward, but since the y is negative, we can classify it as downward, if its positive, it opens upward.

The vertex is (0,0) because if there is no constant value, then the vertex is automatically (0,0). In order to find the other remaining questions, we need to get a, which is the distance of the vertex to the focus.

formula for parabola with vertex (0,0)

x²=-4ay

x²=-7/2y

x²=-4(7/8)y

a=7/8

The focus is (0,-a) which is (0,-7/8)

The directrix is y=7/8

the endpoints of latus rectum is (-7/4,-7/8) and (7/4,-7/8)

If the x is squared, then it opens either upward or downward, but since the y is negative, we can classify it as downward, if its positive, it opens upward.

The vertex is (0,0) because if there is no constant value, then the vertex is automatically (0,0). In order to find the other remaining questions, we need to get a, which is the distance of the vertex to the focus.

formula for parabola with vertex (0,0)

x²=-4ay

x²=-7/2y

x²=-4(7/8)y

a=7/8

The focus is (0,-a) which is (0,-7/8)

The directrix is y=7/8

the endpoints of latus rectum is (-7/4,-7/8) and (7/4,-7/8)