Can I have an explanation on how to do this question? x^2=2x+8,
Let's see x^2 - 2x=8
x^2 -2x -8=0, then you factor it as follows:
(x -4) * (x +2)=0, so that:
x=4 and x=-2
It's a simutaneous equation. If you solve it, it will give you the x coordinates of the intercepts between y = x^2 and y = 2x + 8.
To solve; put it all on one side, so it is equal to 0;
x^2 = 2x + 8
0 = x^2 - 2x - 8
then factorise and use null law to solve;
-4 and 2 multiple to -8, and add to -2
0 = (x-4)(x+2)
x = 4 and -2 so 4 and -2 are x coordinates of intercepts. To find full intercepts, sub these values into 1 of the original equations. Either will work, so just choice easiest:
y = x^2 , x = 4
y = (4)^2
y = 16, therefore (4,16) is intersection of graphs
y = x^2 , x = -2
y= (-2)^2
y = 4, therefore (-2, 4) is the other intersection
