Explore the sliders for \(a\), \(h\), and \(k\) to see how changing these values impacts the graph of the parabola.

Graphing Quadratic Functions | Desmos

Note that \(a = 0\) to begin with. Would you still consider this a quadratic function if \(a\) is 0? Why or why not?

A quadratic function can be written, as shown in the “slider” function in red below.

\(y=a(x-h)^2+k\)

What do you notice about the parabola as \(a\) changes? What do you wonder?

What do you notice about the parabola as \(h\) changes? What do you wonder?

What do you notice about the parabola as \(k\) changes? What do you wonder?

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