Answer
vertex: $\left(\frac{2}{3}, -3\frac{1}{3}\right)$
axis of symmetry: $x=\frac{2}{3}$
minimum value: $-3\frac{1}{3}$
range: $y\ge -3\frac{1}{3}$
Work Step by Step
Use a graphing utility to graph the given function.
Refer to the graph below.
The vertex is the lowest or highest point on the parabola.
Notice that the vertex is at $\left(\frac{2}{3}, -3\frac{1}{3}\right)$.
The axis of symmetry of the graph is the line $x=h$ where $h$ is the $x$-coordinate of the vertex. Thus, the axis of symmetry is $x=\frac{2}{3}$.
The parabola opens upnward so the $y$-coordinate of the vertex is the minimum value.
Hence, the minimum value is $-3\frac{1}{3}$.
The values of the function are all greater than or equal to $-3\frac{1}{3}$.
Thus, the range is $y\ge -3\frac{1}{3}$.
vertex: $\left(\frac{2}{3}, -3\frac{1}{3}\right)$
axis of symmetry: $x=\frac{2}{3}$
minimum value: $-3\frac{1}{3}$
range: $y\ge -3\frac{1}{3}$
