Chapter 3 - Linear and Quadratic Functions - 3.3 Quadratic Functions and Their Properties - 3.3 Assess Your Understanding - Page 145: 10

True.

If the discriminant is $0$, then the the quadratic function has $1$ real number solution. The quadratic function's graph will touch the $x$-axis at the vertex of the graph because the equation $f(x)=0$ will only have $1$ solution. Hence, the given statement is true.