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Question: Find the equation of a function whose graph is a parabola with an axis of symmetry of x = 5.
A ) y = a(x - 5)2 - k
B ) y = a(x + 5)2 + k
C ) y = a(x + 5)2 - k
D ) y = a(x - 5)2 + k
Steps to derive
1 The vertex form of equation of a parabola is given by, y = a(x - h)2 + k, where (h, k) is the vertex and x = h is the axis of symmetry.
2 We are given the axis of symmetry as x = 5 ⇒ h = 5
3 y = a(x - 5)2 + k
[Substitute the values.]
4 So, y = a(x - 5)2 + k, is a function whose graph is a parabola with an axis of symmetry of x = 5.
Hence the right answer is Option D
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