Answer:
[tex]\large\boxed{y=-\dfrac{1}{2}(x-2)^2+4}[/tex]
Step-by-step explanation:
The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have the vertex (2, 4). Substitute:
[tex]y=a(x-2)^2+4[/tex]
The y-intercept (0, 2). Put the coordinates of the y-intercept to the equation:
[tex]2=a(0-2)^2+4[/tex]
[tex]2=a(-2)^2+4[/tex] subtrzct 4 from both sides
[tex]-2=4a[/tex] divide both sides by 4
[tex]-\dfrac{1}{2}=a\to a=-\dfrac{1}{2}[/tex]
Finally:
[tex]y=-\dfrac{1}{2}(x-2)^2+4[/tex]
