The graphs of the equations y = x? +4x-1
and y+3=x are drawn on the same set of axes. At which point do the graphs intersect?
We start by setting the two equations equal to each other and solve for x:
y = x^2 + 4x - 1
y + 3 = x
x^2 + 4x - 1 = x + 3
x^2 + 3x - 4 = 0
(x+4)(x-1) = 0
Solving for x gives x = -4 or x = 1.
To find the corresponding y-coordinates we substitute x into either of the two equations:
y = x^2 + 4x - 1
For x = -4, y = (-4)^2 + 4(-4) - 1 = 9
For x = 1, y = 1^2 + 4(1) - 1 = 4
Therefore, the graphs intersect at the point (-4,9) and (1,4).