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Question

If the vertex of the parabola y = x2 – 16x + k lies on x-axis, then k = __________.

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Solution

Given parabola is,
y = x2 − 16x + k
= x2 − 2x(8) + k
= x2 − 2x(8) + 64 − 64 + k
y = (x − 8)2 − 64 + k
Since parabola has vertex an x - axis
⇒ −64 + k = 0
i.e. k = 64

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