Just knowing those two points we can come up with an equation.
Firstly, we know h and k (at the vertex):
(h, k) = (1,1)
So let's put that into this form of the equation:
f(x) = a(x-h)2 + k
f(x) = a(x-1)2 + 1
Then we calculate "a":
And so here is the resulting Quadratic Equation:
f(x) = 0.5(x-1)2 + 1
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