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