A parabola is a type of U-shaped curve defined by an equation of the form y=ax²+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=ax²+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 = ax² + 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=-1/25x²+3.

The above graph shows the parabola with a vertex at (5, 3), as determined by the equation y=-1/25x²+3.