+743 Three points lie on the graph of the parabola $y = x^2$. The three points form an equilateral triangle. One of the vertices is at the vertex of the parabola, and the other two points lie on the line $y = k$. What is the value of $k?$
+129881 We can find the intersection of the line y = sqrt (3)x and the parabola to give us the answer
x^2 = sqrt (3)x
x^2 - sqrt (3)x = 0
x ( x - sqrt 3) = 0
Setting the second factor to 0 and solving for x produces the x coordinate of one of the intersections = sqrt 3
The y coordinate is y= x^2 = (sqrt 3)^2 = 3 = k
