# FNGR 2 | Lesson 2 | Explore (Graphing Quadratic Functions) Solutions

1. The vertex of the parabola $$y=x^2$$ is (0, 0).  This makes sense because when $$x=0$$, then $$y=0^2$$, and then $$y=0$$
2. The parent parabola $$y=x^2$$ opens up.
3. For a parabola written in standard form, when $$a = 0$$, the result is a line.  This makes sense because if the squared term is zero, then the result is a linear equation.
4. When $$a > 0$$, the graph opens up.  When $$a < 0$$, the graph opens down.  When $$|a| > 1$$, the shape of the graph is stretched (wider).  When $$|a|$$ is between 0 and 1, then the shape of the graph is compressed (narrower).  Changing $$b$$ moves the location of the parabola in an arch around the original vertex, but it does not change the shape.  Changing $$c$$ moves the location of the parabola up or down, but it does not change the shape.