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Question

If the vertex of the parabola y=x216x+k lies on x−axis, then k=

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Solution

Equation of parabola : y=x216x+k
y=(x8)264+k
y+64k=(x8)2
(x8)2=4×14(y+64k) (1)
For coordinate of vertex,
x8=0 and y+64k=0
x=8 and y=k64
Vertex, V=(8, k−64)
Since vertex lies on the x− axis,
k64=0
k=64
Hence, if the vertex of the parabola y=x216x+k lie on x−axis, then k = 64.

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