Question

the line y=2x-4 and the parabola y=x^2- 4 intersect in the standard x,y coordinate plane if point a s,t is at an intersection of the line and the parabola what is the greatest possible value of s?

Answer 1

2x-4=x^2-4
-4=x^2-2x-4 (start moving everything to one side)
x^2-2x=0 (the 4 cancel out)
x(x-2)=0 (factor out an x)
x=0 & x=2 (solved for x)

y=2x-4 (pick one of the equations)
y=2(0)-4 (plug in x)
y=-4
(0,-4)

y=2(2)-4 (plug in the second point)
y=0
(2,0)

The greatest possible value of s is 2. (2,0)