8/16/2014 For what value(s) of K will the parabola y² – 6y + x + K = 0 have exactly 1 y-intercept? Find the intercept.For what value(s) of K will the parabola y² – 6y + x + K = 0 have exactly 1 y-intercept? Find the intercept.

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8/16/2014 Solution. At the y-intercept(s), x = 0 so that: y² – 6y + K = 0.

For the parabola to have exactly 1 y-intercept: b² – 4ac = 0 => 36 – 4K = 0.

Therefore, K = 9.

At K = 9, the y-intercept is: y² – 6y + 9 = 0 => (y – 3)² = 0 => y = 3