Like if i was givin a graphed parabola how would i figure out how to write the equation, in vertex form/

Some examples for the formula

The format of the equation that shows you where the vertex is

y = a(x - h)

^{2}+ kExample. This parabola has a vertex at (3,4).

y = 2(x - 3)

^{2}+ 4Example 2. This parabola has a vertex at (1,1)

y = (x–1)² + 1

How to find "a"???

Pick a point on the graph other than the vertex. Let's say you see the line pass through (1,5) and the vertex is at (3,4)...

First the vertex gives you this...

y = a (x - 3)

^{2}+ 4Put the values (1,5) into this equation.

5 = a (1 - 3)

^{2}+ 4Solve for a

5 = a*(-2)

^{2}+ 45 = 4a + 4

1 = 4a

1/4 = a

Final equation is

y = 1/4*(x - 3)

^{2}+ 4