FYI: Different textbooks have different interpretations of the reference "standard form" of a quadratic function. Some say f (x) = ax2 + bx + c is "standard form", while others say that f (x) = a(x - h)2 + k is "standard form". To avoid confusion, this site will not refer to either as "standard form", but will reference f (x) = a(x - h)2 + k as "vertex form" and will reference f (x) = ax2 + bx + c by its full statement.
When written in "vertex form": • the h represents a horizontal shift (how far left, or right, the graph has shifted from x = 0). • the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0). • notice that the h value is subtracted in this form, and that the k value is added.
Convert y = 2x2 - 4x + 5 into vertex form, and state the vertex.
Method 2: Using the "sneaky tidbit", seen above, to convert to vertex form:
To Convert from Vertex Form to y = ax2 + bx + c Form:
Graphing a Quadratic Function in Vertex Form:
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Vertex Form of Quadratic Equation (2024)
References
- https://mathbitsnotebook.com/Algebra1/Quadratics/QDVertexForm.html
- https://www.mathebibel.de/ableitungsregeln
- https://www.maths2mind.com/schluesselwoerter/hyperbelfunktionen
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