Points of intersection of linear graphs an quadratic graphs Quadratic Equations Points of intersection of linear graphs an quadratic graphs

Find the solutions for y = x2 – 2x + 2 and y = 7 Quadratic Equations Finding solutions Find the solutions for y = x2 – 2x + 2 and y = 7 We draw the quadratic curve y = x2 – 2x + 2 and the line y = 7 The solutions are where the quadratic curve crosses the straight line y = 7

Quadratic Equations Solutions are x = -1.45 and x = 3.45 y = 7

Now review the solutions to x2 – 2x – 5 = 0 Quadratic Equations Now review the solutions to x2 – 2x – 5 = 0 Solutions are x = -1.45 and x = 3.45 Is this a coincidence?

The solutions for y = x2 – 2x + 2 and y = 7 are where x2 – 2x + 2 = 7 Quadratic Equations The solutions for y = x2 – 2x + 2 and y = 7 are where x2 – 2x + 2 = 7 Rearrange the equation by subtracting 7 from both sides x2 – 2x – 5 = 0

Quadratic Equations y = x2 – 2x + 2 -7 y = x2 – 2x - 5 If we rearrange the equation we find that we have the same solutions because the process of rearranging translates (moves) the graph

This applies to the intersections of other lines Quadratic Equations This applies to the intersections of other lines Show where the curve of y = x2 + 2x – 4 crosses the line y = x - 3 Solutions are x = -1.6 x = 0.6

The solutions for y = x2 – 2x - 4 and y = x - 3 Quadratic Equations The solutions for y = x2 – 2x - 4 and y = x - 3 are where x2 – 2x - 4 = x - 3 Rearrange the equation - x from both sides x2 –3x - 4 = - 3 + 3 to both sides x2 –3x - 1 = 0 The solutions to this will be the same as the solutions to x2 – 2x - 4 = x - 3