A parabola is a type of U-shaped curve defined by an equation of the form *y=ax ^{2}+bx+c*. It has a shape that is symmetrical about a line called the

**axis of symmetry**, and the point at which the axis passes through the parabola is called the

**vertex**.

If the vertex of a parabola is known, then the equation of that parabola can be found by substituting the coordinates of the vertex into the equation. For example, if the vertex of a parabola is *(5, 3)*, then the equation for that parabola would be *y=ax ^{2}+bx+c*, where

*a*,

*b*, and

*c*are constants that can be determined by substituting

*x=5*and

*y=3*into the equation.

To do this, first we need to expand the equation:

y = ax^{2} + bx + c

3 = a(5)^{2} + b(5) + c

3 = 25a + 5b + c

Now, we can solve for the constants *a*, *b*, and *c*:

a = -1/25

b = 0

c = 3

Therefore, the equation of the parabola with a vertex at *(5, 3)* is *y=-1/25x ^{2}+3*.

The above graph shows the parabola with a vertex at *(5, 3)*, as determined by the equation *y=-1/25x ^{2}+3*.