Finding the Vertex in Vertex Form

9.9.1 Finding the Vertex in Vertex Form

9.9.1 • Finding the Vertex in Vertex Form

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).

Compare your answer:

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

Minimum

What is the axis of symmetry?

Compare your answer:

$x = - 3$