Question

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

Answer 1

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.