 Case 3: One Solution (Line is a Tangent) Line: y = 4x - 7 Parabola: y = 2x2 - 8x + 11 Graphical Solution:
The point of intersection appears to be (3, 5). This is already in the parabola table; checking in the line equation shows that it works there too. Solution (3, 5) Algebraic Solution: y = 4x - 7 y = 2x2 - 8x + 11 Using the Comparison method: 2x2 - 8x + 11 = 4x - 7 2x2 - 12x + 18 = 0 Solve by factoring: 2(x2 - 6x + 9) = 0 2(x - 3)2 = 0 x = 3 Substitute in line equation: y = 4(3) - 7 = 5 Solution (3, 5) Finally let's look at the case where there are two solutions >>> |
