which point is definitly on this parabola?

Question

Vertex of a parabola is on y axis. and the point (4,7) is on this parabola.

which one of these points definitly on the parabola : (-4,7),(2,7),(0,11),(-2,7) or (0,-5)

Let $(0,b)$ be the vertex point. so the equation should be $y=ax^2+b$ or $x=c(y-b)^2$ so There are 4 possible parabolas

$16a+b=7$

$4=c(7-b)^2$

$c=\frac{1}{64a^2}$

shouldnt it give us more information?

Answer 1

Although the parabola is not completely described, you do have enough information to check whether one of the listed points is on the parabola. Specifically, $(-4,7)$ must be on the parabola because its center is on the y-axis.

Regarding the other points: $(2,7)$ cannot be on the parabola because it conflicts with $(4,7)$ (and by extension neither can $(-2,7)$). Either $(0,11)$ or $(0,-5)$ might be the vertices but you can't say for sure.