The graph of the function Y = X ^ 2 + k * X + 4 is a parabola.
Since, by condition, the parabola touches the OX axis, the quadratic equation X ^ 2 + k * X + 4 = 0 has one root, and therefore the discriminant D = 0.
D = b ^ 2 – 4 * a * c = 0.
D = k ^ 2 – 4 * 1 * 4 = 0.
k ^ 2 = 16.
k = ± 4.
k1 = 4.
k2 = -4.
Answer: When k1 = 4, k2 = -4, the curve touches the OX axis.
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