Question

Why is the vertex of vertex form y=a(x-h)^2+k (h,k) rather than (-h,k)? If that was y=2(x-5)^2+6, the vertex would be at (5,6) which is (-h,k).​

Answer 1

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Answer:

(5, 6) is (h, k)

Explanation:

Vertex form is an instance of the transformation of parent function f(x) = x². It is vertically scaled by a factor of 'a', and translated so the vertex is point (h, k). That is, the transformed vertex is h units right and k units up from that of the parent function (0, 0).

Parent:

f(x) = x^2

Transformed:

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

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When you compare the form to your specific instance, you need to pay attention to what it is that you're comparing. As the attachment shows, ...

• a = 2
• -h = -5 ⇒ h = 5
• k = 6

Hence the vertex is (h, k) = (5, 6). The second attachment shows this on a graph.