Answer
This statement is true.
Work Step by Step
To find the intercepts with $x$ axis (if they exist) put $y=0$ in the equation and calculate $x$. The obtained values for $x$ will determine where the graph intercepts the $x$ axis:
$$ax^2+bx+c=0.$$
This is a quadratic equation in $x$ and its' solutions are given by quadratic equation formula
$$x_{1,2} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}.$$
Since $b^2-4ac=0$ then also $\sqrt{b^2-4ac} = 0$ so in the formula for $x_{1,2}$ we actually have
$$x_{1,2} = \frac{-b\pm0}{2a} = -\frac{b}{2a}$$
so there is only one solution since it doesn't matter whether we add or subtract $0$. So the only intercept with the $x$ axis will occur in $$x=-\frac{b}{2a}$$ and the statement is true.
