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Question

Write down an equation for a parabola that has a vertex at (4,2)

Answer 1

most standard parabola would be upward opening

y=(x-4)^2 + 2 where y=(x-h)^2+k and (h,k) is the vertex and minimum point

but you could

have a downward opening parabola with the same vertex

y=-(x-4)^2+2 Just put a negative sign in

or a leftward opening parabola

x =-(y-2)^2 + 4

or a rightward opening parabola

x=(y-2)^2 +4

all have the same vertex (4,2)

there's also an infinite number of other parabolas, at different angles, all with the same vertex