Answer:

Step-by-step explanation:
A parabola is written in the form
 (1)
 (1)
where:
 is the x-coordinate of the vertex of the parabola
 is the x-coordinate of the vertex of the parabola
 is the y-coordinate of the vertex of the parabola
 is the y-coordinate of the vertex of the parabola
 is a scale factor
 is a scale factor
For the parabola in the problem, we know that the vertex has  coordinates (4,-3), so we have:
 (2)
 (2)

From this last equation, we get that  (3)
 (3)
Substituting (2) and (3) into (1) we get the new expression:
 (4)
 (4)
We also know that the parabola  contains the point (2,-1), so we can substitute
x = 2
f(x) = -1
Into eq.(4) and find the value of k:

So we also get:

So the equation of the parabola is:
 (5)
 (5)
Now we want to rewrite it in the standard form, i.e. in the form

To do that, we simply rewrite (5) expliciting the various terms, we find:
