Any horizontal lineabove the x-axis will intersect this parabola twice. For example, let's consider the line y=1.
We can see that the line and the parabola have two points of intersection. Therefore, the system formed by the equations of the above graphs will have two solutions.
y=x^2 y=1
Note that there are infinitely many systems that satisfy the given condition. This is only one of them.
b Just as we did in Part A, we will consider the graph of the quadratic function y=x^2.
Note that the above parabola intersects the x-axis at exactly one point. The x-axis can be thought of as the line y=0.
Therefore, the system formed by the equations of the above graphs will have exactly one solution.
y=x^2 y=0
Note that there are infinitely many systems that satisfy the given condition. This is only one of them.
c One last time, we will consider the graph of y=x^2.
No horizontal line below the x-axis will intersect this parabola. As an example, let's consider the line y=- 1.
We can see that the line and the parabola do not intersect. Therefore, the system formed by the equations of the above graphs will have no solutions.
y=x^2 y=- 1
Note that there are infinitely many systems that satisfy the given condition. This is only one of them.
