Write and equation of the parabola in vertex form. Vertex equals (0,3) (1,-4)

Question

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Answer 1

(0,3), (1,-4) suggests the 1st is the vertex and (1,-4) another point on the parabola

y = ax^2 +3, plug in the 2nd point to solve for "a"

-4 = a +3

a = -7

parabola is downward opening

y = -7x^2 +3

but there are actually an infinite number of possible parabolas,

another standard one is right ward opening, a horizontal parabola

but only the vertical parabola is a function

x =a(y-3)^2

1 =a(-4-3)^2 = 49a

a = 1/49

x = (1/49)(y-3)^2