QuestionDecide whether the following statement is true or false. If the discriminant $b^{2}-4 a c=0$, the graph of $f(x)=a x^{2}+b x+c, a \neq 0$, will touch the $x$-axis at its vertex.
Choose the correct answer below. True False

Studdy Solution
The vertex of the parabola $f(x) = ax^2 + bx + c$ is at $x = -\frac{b}{2a}$. When the discriminant is zero, the double root occurs at this vertex. Therefore, the graph of the function touches the x-axis at its vertex.
The statement is:
True