A quadratic function with a discriminant of 0 only touches the x-axis, hence it is represented by the fourth graph.
What is the discriminant of a quadratic equation and how does it influence the solutions?
A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
- If [tex]\mathbf{\Delta > 0}[/tex], it has 2 real solutions, hence it crosses the x-axis twice.
- If [tex]\mathbf{\Delta = 0}[/tex], it has 1 repeated solution, hence it touches the x-axis.
- If [tex]\mathbf{\Delta < 0}[/tex], it has 2 complex solutions, hence it does not touch the x-axis.
In this problem, the fourth graph touches the x-axis, hence it is the answer to this question.
More can be learned about quadratic functions at https://brainly.com/question/24737967
