Varying d in the Equation

In this investigation, I would like to see what happens to the graph of the given function by changing the value of d.

First, I will graph the function with d = -2, -1, 0, 1, 2.

All of the graphs have a vertex with a y-value of -2. Does this come from the - 2 at the end of each equation? What happens if it is a + 2 instead?

This leads me to believe that a quadratic equation written in this form will have a vertex with a y-value of the number added to the end.

click here to see this investigation as a movie. (I have let d=0 and am calling the number added to the end k. I let k run from -5 to 5.)

Back to the question at hand -- what happens when the value of d is changed?

If d =1, we have:

This graph has a vertex (1,-2).

If d = 2, we have:

This graph has a vertex (2,-2).

If d = 3, we have:

This graph has a vertex (3,-2).

If d = -1, we have:

This graph has a vertex (-1,-2).

If d = -2, we have:

This graph has a vertex (-2,-2).

I think that it becomes very obvious that whenever you have a quadratic equation in this form, the vertex will lie at: (d,k).

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