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Changing the value of p in Parabola equation y=a(x-p)^2+q

Q: What happens if I change the value of p?

A: p is the x-coordinate of your vertex. If it changes, the parabola will shift left or right.

Note that the general equation for a parabola is y=a(x-p)^2+q

(x-p) means:

  • if you have a positive p value, the result will be (x-p)
  • if you have a negative p value, the result will be (x-(-p))=(x+p)

Let’s take a look at what happens when p=3, and then what happens when p=-3.

Parabolas with different p values