The parabola equation in vertex form is given by:
[tex]\begin{gathered} y=a(x-h)^2+k \\ h\colon\text{horizontal coordinate of the vertex} \\ k\colon\text{vertical coordinate of the vertex} \end{gathered}[/tex]
From the given question, we are provided with the following:
[tex]\begin{gathered} \text{vertex (1,-5)} \\ \text{point (x,y)= (-4,3)} \end{gathered}[/tex]
We have to use the given parameters to find the parameter 'a' from the parabola equation.
Thus, we have:
[tex]\begin{gathered} y=a(x-h)^2+k \\ 3=a(-4-1)^2+(-5)^{} \\ 3=a(-5)^2-5 \\ 3+5=25a \\ 25a=8 \\ a=\frac{8}{25} \end{gathered}[/tex]
Hence, the equation of the parabola is:
[tex]\begin{gathered} y=\frac{8}{25}(x-1)^2+(-5) \\ y=\frac{8}{25}(x-1)^2-5 \end{gathered}[/tex]
The graph of the parabola on the xy-plane is shown below:
