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Find the equation for a parabola that has a vertex at (0, 4) and passes through the point (–1, 6).

User Asad Malik
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1 Answer

3 votes

Answer:


\large\boxed{y=2x^2+4}

Explanation:

The vertex form of a parabola:


y=a(x-h)^2+k

(h, k) - vertex

We have the vertex at (0, 4) → h = 0 and k = 4.

Substitute:


y=a(x-0)^2+4=ax^2+4

The point (-1, 6) is on the parabola. Put the coordinates of the point to the equation:


6=a(-1)^2+4 subtract 4 from both sides


2=a\to a=2

Finally:


y=2x^2+4

User Scott Buchanan
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7.5k points