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.
Method 2: Using the "sneaky tidbit", seen above, to convert to vertex form:
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Vertex Form of Quadratic Equation (2024)
References
- https://www.physicsforums.com/threads/heaviside-function-clarifying-h-x-a-h-a-x.897213/
- https://math.libretexts.org/Bookshelves/Algebra/College_Algebra_1e_(OpenStax)/05%3A_Polynomial_and_Rational_Functions/502%3A_Quadratic_Functions
- https://mathbitsnotebook.com/Algebra1/Quadratics/QDVertexForm.html
- https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:vertex-form/v/graphing-a-parabola-in-vertex-form
- https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/v/function-composition
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