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

2. 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

3. Quadratic Equations
Solutions are
x = and x = 3.45
y = 7

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

5. 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

6. 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

7. 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

8. 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