9.9.1 Finding the Vertex in Vertex Form

Algebra 19.9.1 Finding the Vertex in Vertex Form

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9.9.1 • Finding the Vertex in Vertex Form

Warm Up

Write the quadratic function $f (x) = x^{2} + 6 x + 13$ in vertex form.

Compare your answer:

$f (x) = (x + 3)^{2} + 4$

$(\frac{b}{2})^{2} = (\frac{6}{2})^{2} = \frac{36}{4} = 9$

$f (x) = x^{2} + 6 x + 9 + 13 - 9$

$f (x) = x^{2} + 6 x + 9 + 4$

$f (x) = (x + 3)^{2} + 4$

Using the vertex form of the quadratic found in question 1, what is the vertex?

Compare your answer:

$(- 3, 4)$

Graph both equations from question 1 (in standard form and vertex form).

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Compare your answer:

Graph of a parabola on a coordinate plane. The x-axis has a scale of 1 extending from negative 9 to 5. The y-axis extends from negative 3 to 10 with a scale of 1. The coordinates of the vertex have been labeled.

Determine if the vertex for the quadratic function is a maximum or minimum.

Minimum

What is the axis of symmetry?

Compare your answer:

$x = - 3$

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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
- Location: Houston, Texas
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- Section URL: https://openstax.org/books/algebra-1/pages/9-9-1-finding-the-vertex-in-vertex-form

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