Note that the function is expressed in vertex form. Let's compare the general formula for the vertex form with our function. We can see that and Recall that the vertex of a quadratic function written in vertex form is the point Therefore, the vertex of the given equation is Let's plot the vertex on a coordinate plane.
The axis of symmetry of a quadratic function written in vertex form is the vertical line with equation As we have already noticed, for our function, this is Therefore, the axis of symmetry is the line
The axis of symmetry divides the parabola into two mirror images. Therefore, points on one side of the parabola can be reflected across the axis of symmetry. Notice that the intersection with the vertical axis is units away from the axis of symmetry. Thus, there exists another point directly across the axis of symmetry that is also units away, in the opposite direction.
Now, with three points plotted, the general shape of the parabola can be seen. It appears that the parabola faces upward. Since in the given function rule, this should be expected. To draw the parabola, we will connect the points with a smooth curve. Note that negative values for do not make sense. We will draw the curve for