Question

Find the coordinates of the points of intersection of the parabola y=x^2+3x-4 and the line y=2x+2

Answer 1

You can set the y values equal to each other and solve the system:

x^2+3x-4=2x+2
x^2+x-6=0
(x+3)(x-2)=0
x=-3,2

So, these are the x values of the intersection. To get the y values, you can just plug them back into either formula:

y=2(-3)+2
y=-4

y2(2)+2
y=6

So the coordinates are (-3,-4) and 2,6).