Posted by **Anup** on Monday, May 23, 2011 at 7:52pm.

there are ___ parabolas that have a vertex (-3,-4) and pass through the point (-1,4)

- math -
**Henry**, Tuesday, May 24, 2011 at 7:02pm
We shall attempt to derive the Eq of an

X-parabola and a Y-parabola using the

given vertex and point.

V(-3,-4), P(-1,4).

Vertex Form: X = a(Y-K)^2 + h.

X = a(4-(-4))^2 -3 = -1,

64a - 3 = -1,

64a = -1 + 3 = 2,

a = 2/64 = 1/32.

Eq: X = (1/32)(Y+4)^2 - 3.

Therefore an X-parabola with the given

vertex passes through the point given.

Y = a(X-h)^2 + K.

Y = a(-1-(-3))^2 - 4 = 4,

4a - 4 = 4,

4a = 8,

a = 2.

Eq: Y = 2(X+3)^2 - 4.

Therefore, a Y-parabola with the given

vertex passes through the givn point.

Answer: 2 parabolas.

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