Show the curve y = 4x^2 + 5x + 3 and the line y = x + 2 have exactly one point of intersection
The curve and the line will intersect when the two expressions are equal, so:4x2+ 5x + 3 = x + 2 (eliminating y and putting the expressions in terms of one variable).4x2+ 4x + 1 = 0(2x + 1)2 = 0 (would note here that we are asked to show they intersect at only one point so would expect a single linear expression raised to a power)Therefore, x = -1/2; and as y = x + 2, y = 3/2. So our single point of intersection is (-1/2, 3/2).
