Answer
Please see the graph.
Work Step by Step
$H(x)=(x+1/4)^2−3$
Axis of symmetry:
$H(x)=(x+1/4)^2−3$
$H(x)=(x− −1/4)^2−3$
$x=−1/4$
Vertex:
$H(x)=(x+1/4)^2−3$
$H(−1/4)=(−1/4+1/4)^2−3$
$H(−1/4)=(0)^2−3$
$H(−1/4)=−3$
The red line is the function $H(x)=(x+1/4)^2−3$, the line at $x=−1/4$ is the axis of symmetry, and the point $(−1/4,−3)$ is the vertex.
