Create a quadratic equation. Give an example of a linear equation that, when put into a system with your created quadratic equation, will have two solutions, one solution and no solutions.

Question

1. Give an example of a linear equation that, when put into a system with your created quadratic equation, will have two solutions. Include the work that shows the two solutions.
2. Give an example of a linear equation that, when put into a system with your created quadratic equation, will have one solution. Include the work that shows the solution.
3. Give an example of a linear equation that, when put into a system with your created quadratic equation, will have no solutions. Include the work that shows there are no solutions.

Answer 1

1. y = x2 - 9 Intersection

y = x -3 (x-3)= x^2-9 = (x-3)(x+3) 1=x+3 x=-2 (-2,-5)

2. y = x2 - 9

y = 10x 10x = x^2 - 9 x^2-10x-9 = 0 x=-.83 (-.83,-8.3)

3. y = x2 - 9 These 2 equations do not intersect. None

y = x - 10

Answer 2

Here are the very easy equations that fit this problem:

Quadratic equation: y = x²

System with two solutions:

y = x²

y = 1 (red line)

y = x²

1 = 1² and 1 = (-1)²

The two solutions: (1,1) and (-1,1)

System with one solution:

y = x²

y = 0 (blue line)

0 = (0)²

The one solution is (0,0)

No solution to system:

y = x²

y = x - 1

There is no square of a number that is one less than the original number.