"Quadratic functions have Answer 1 Question 1 when the vertex is the only point that touches the x𝑥-axis."

Quadratic functions have one real root when the vertex is the only point that touches the x-axis.

Here's the step-by-step explanation:

1. A quadratic function is a function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

2. The graph of a quadratic function is a parabola. The vertex of the parabola is the point where the parabola turns; it is the maximum or minimum of the function.

3. If the vertex of the parabola is the only point that touches the x-axis, that means the parabola just touches the x-axis at one point and does not cross it.

4. The points where a parabola crosses the x-axis are the roots of the corresponding quadratic function.

5. Therefore, if the vertex is the only point that touches the x-axis, the quadratic function has exactly one real root. This root is also called a double root or a repeated root.