# Graphing Quadratic Functions

Consider the graph of the quadratic parent function $$y=x^2$$.

1. What is the vertex of this parabola?
2. Does this parabola open up or down?

Go to the Desmos activity below to explore how changing the values of $$a$$, $$b$$, and $$c$$ impact the graph a parabola written in Standard Form $$y=ax^2 + bx + c$$.

Graphing Quadratic Functions | Desmos

3. What happens when $$a = 0$$?  Why does this make sense?

4. What can you generalize about the shape and location of a parabola written in standard form when the values of $$a$$, $$b$$, and $$c$$ change?

Check solutions here.