9.9.4 Rewriting Quadratics

Algebra 19.9.4 Rewriting Quadratics

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Activity

For questions 1 - 2, use the function $f (x) = x^{2}$ that is shifted to create the function $g (x)$ that has a vertex at $(3, - 2)$ .

Write $g (x)$ in vertex form.

Compare your answer:

$g (x) = (x - 3)^{2} - 2$ The vertex form of a quadratic is $f (x) = a (x - h)^{2} + k$ . Since there is not a vertical stretch or compression or reflection mentioned, the vertex values are substituted for $(h, k)$ . $g (x) = (x - 3)^{2} + - 2$ becomes $g (x) = (x - 3)^{2} - 2$ .

Write $g (x)$ in standard form.

Compare your answer:

Compare your answer: $g (x) = x^{2} - 6 x + 7$ $g (x) = (x - 3)^{2} - 2$ $g (x) = (x - 3) (x - 3) - 2$ $g (x) = x^{2} - 3 x - 3 x + 9 - 2$ $g (x) = x^{2} - 6 x + 7$

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
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- Book title: Algebra 1
- Publication date: Jun 4, 2025
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