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# What is the vertex of a parabola in the form of the equation y=a(x – h)2 + k?

(a, k)

(a, h)

(h, k)

(h, –k)

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- Anonymous9 years agoFavorite Answer
(h, k)

Explanation:

y = a*(x – h)^2 + k

If x = h, then

y = a*(h – h)^2 + k

y = a*(0)^2 + k

y = k

Notice that when the term a*(x – h)^2 = 0, y is a minimum at y = k. For example, if x = h + 1, then

y = a*(x – h)^2 + k

y = a*((h + 1) – h)^2 + k

y = a*1^2 + k

y = a + k

Therefore, if a > 0 i.e. the parabola has upward orientation, then a + k > k. Therefore, y = k is the lowest value that y can take. As a result, (h, k) is the vertex of your parabola.

In the other case, if a < 0 i.e. the parabola has downward orientation, then a + k < k. Therefore, y = k is the highest value that y can take. In either case, (h, k) is the vertex of the parabola.

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- Anonymous9 years ago
The correct answer is (h,k)

I hope this helps!

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