Exploring the equation ax² + bx + c = y

 

Let b = 1 and c = 1, below is an example of graphs as 'a' changes:

(insert graph)

Notice that every parabola shares the same vertex. The only difference is the size of the parabola. The larger our value for 'a' the narrower the parabola becomes, as if it is being stretched vertically. When 0 < a < 1, the parabola is much wider.

 

Let a = 1 and c = 1, below is an example of graphs as 'b' changes:

(insert graph)

Each of these graphs appears to be congruent. It almost looks like they have been shifted horizontally.

Each of these graphs also intersect the y-axis at 1. Is this a result of b? Or is it coincidence? Let's answer this by considering what happens when we alter the value of 'c.'

 

Let a = 1 and b = 1, below is an example of graphs as 'c' changes:

(insert graph)

From the graph and the equation we notice that the value of 'c' is where the parabola of interesects the y-axis.

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