How can I find the coordinates of the points at the curve yx

How can I find the coordinates of the points at the curve y=x2-x-12 where it cuts the x axis and y axis?

Solution

To find the coordinates of the points of intersection of the curve y=x^2-x-12 with x and y axes.

The equation of x axis is y=0. Therefore,the points of intersection of y=x^2-x-12 and y=0 are got by eliminating y between these two equations or putting y=0 in y= x^2-x-12 and solving for x to get x intercepts:

0 =x^2-x-12

0=(x+3)(x-4). or x+3=0 or x-4=0 ==>

x=-3   or x=4, are the points on x axis where the curve intersects x axis. So, the coordinates of the points of intersection of x axis are (-3 , 0) and (4 , 0)

Similarly the equation of y axis is x=0. So,Put x= 0 in y = x^2-x-12 and solve for y to get the point , where the given curve intersects y axis: So,

y=0^2-0-12 =-12, is the point where the curve intersects y axis. So, the coordinates of the point of intersection of y axis is: (0 , -12)