Given the following:
The vertex (0, -1) and it passes through (-4, -5)
We are to write an equation in vertex form and simplify any fraction.
We will start start with the vertex form of the equation of a parabola.
y - k = a(x - h)^2
Since the veryex is at (0, -1), we now have
y + 1 = a(x - 0)^2, or y + 1 = ax^2
The point (-4, -5) is on this parabola, Therefore,
-5 + 1 = a(-4)^2
-4 = a*16
making a subject of formular
a = -4/16
a = -1/4
Therefore, the desired equation is y + 1 = (-1/4)(x - 0)^2