What is the Vertex Form for a Quadratic Equation ?

The vertex form for a quadratic function is as follows: f(x) = a(x - h) 2 + k The graph of this function Is a parabola whose axis of symmetry is the vertical line x = h, and whose vertex is the point (h, k).

Remember: If a > 0 then the graph opens upward.

If a < 0 then the graph opens downward.

In order to use the vertex form to find the vertex, you must know how to complete the square.
Here's an example of what I mean by completing the square:

Question: Find the vertex of the graph of

f(x) = x² - 4x + 5

Answer: In order to do this, we must write the function in vertex form.
f(x) = x² -4x + 5
y = x² - 4x + 5
y - 5 = x² - 4x
y - 5 + 4 = x² -4x + 4
y - 1 = (x -2) 2
y = (x - 2)2 + 1
f(x) = (x-2)2 +1
H             k
The vertex of the parabola is then (h, k) = (2, 1)