Identifying Characteristics of Quadratic Functions

Let's begin by finding the vertex of the parabola. Recall that the vertex is the highest or lowest point of the curve and lies on the axis of symmetry.

The parabola opens upward and therefore the vertex is its minimum point. We see the vertex is the point $(2,\text{-}1).$ Next, we will find the equation of the axis of symmetry. The axis of symmetry is the vertical line through the vertex, and divides the parabola into two congruent halves.

The equation of the axis of symmetry is $x=2.$ Finally, we will find the $y\text{-}$intercept, which is the point where the graph intercepts the $y\text{-}$axis.

As we can see, the $y\text{-}$intercept is located at $(0,1).$