Question

Identify the equation of the parabola.

Answer 1

the vertex form of a parabola is
\[y=a(x-h)^2+k\]
What a does
If a> 0, the parabola opens upwards
if a< 0, it opens downwards.

If a is positive then the parabola opens upwards like a regular "U".
If a is negative, then the graph opens downwards like an upside down "U".

(h,k) is the vertex

the vertex in the picture is (0,0), but why is there a dot at x-axis 2?

Answer 2

the dot is the focus... I think

Answer 3

oh, since the parabola is on the axis, the y and x of the vertex form should switch
the previous vertex form of the parabola i showed was for graphs that looks like this
y=a(x-h)^2+k

but your graph should look like this
x=a(y-h)+k