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?

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Check solutions here.

Go to Explore (Vertex Form | Desmos)