Which of the following gives the point of intersection of the graph y = x^{2} and y = x + 6 shown above?

Answer Details

The problem is asking us to find the point of intersection of the two graphs y = x2 and y = x + 6. This can be done by solving the equations simultaneously. We need to find the values of x and y that satisfy both equations.
We can do this by substituting y = x + 6 for y in the equation y = x2, giving us:
x + 6 = x2
Rearranging this equation gives us:
x2 - x - 6 = 0
We can factor this quadratic equation to obtain:
(x - 3)(x + 2) = 0
Thus, the solutions are x = 3 or x = -2.
To find the corresponding values of y, we can substitute these values of x into either of the original equations. For example, if we use y = x + 6, we get:
When x = 3, y = 3 + 6 = 9, giving us the point (3, 9).
When x = -2, y = -2 + 6 = 4, giving us the point (-2, 4).
Therefore, the point of intersection of the two graphs is (3, 9) and (-2, 4).