Mark M. answered • 08/05/20
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y = a(x - h)2 + k
y = a(x - 0)2 + 0
focus: (0, 3)
focus: (0, k + p)
p = 3
a = 1 / 4p
a = 1 / 12
y = (1/12)x2
Katie R.
asked • 08/05/20Find an equation for the parabola that has its vertex at the origin and satisfies the given conditions. Opens upward with focus 3 units from the vertex
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David M.
I would add where the formulatic equation comes from. In general, the implicit equation (y-k)=a*f(x-h) represents a function y=f(x) that has been scaled by a (i.e. values multiplied by a), then shifted horizontally by a, and vertically by k. Solving for y, we get the explicit equation y=a*f(x-h)+k. So, if we start with the parent parabola equation y=x^2, then y=a*(x-h)^2+k scales y=x^2 by a and shifts horizontally by h and vertically by k.08/08/20