In order to find the equation of the parabola, let's use the vertex form below:
[tex]y=a(x-h)^2+k[/tex]
Where the vertex is located at (h, k). If the vertex is located at (2, 5), therefore h = 2 and k = 5.
Now, let's use the point (4, -3) in the equation so we can calculate the value of a:
[tex]\begin{gathered} y=a(x-2)^2+5\\ \\ -3=a(4-2)^2+5\\ \\ -3=4a+5\\ \\ 4a=-8\\ \\ a=-2 \end{gathered}[/tex]
Therefore the equation is:
[tex]y=-2(x-2)^2+5[/tex]
