math
posted by Anup on .
there are ___ parabolas that have a vertex (3,4) and pass through the point (1,4)

We shall attempt to derive the Eq of an
Xparabola and a Yparabola using the
given vertex and point.
V(3,4), P(1,4).
Vertex Form: X = a(YK)^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 Xparabola with the given
vertex passes through the point given.
Y = a(Xh)^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 Yparabola with the given
vertex passes through the givn point.
Answer: 2 parabolas.