Final answer:
The equation of the parabola with vertex at (2, -3) and y-intercept at (0, 5) is y=2(x-2)^2-3.
Step-by-step explanation:
The question asks to write the equation of a parabola given the vertex $(2, -3)$ and its y-intercept $(0,5)$.
To start, the vertex form of the equation of a parabola is $y = a(x-h)^2+k$, where $(h, k)$ is the vertex.
We know the vertex $(h, k) = (2, -3)$.
To find the value of $a$, we can substitute the y-intercept into the equation, which gives us $5=a(0-2)^2-3$.
Solving for $a$ yields $a=2$.
Therefore, the equation of the parabola is $y=2(x-2)^2-3$.