4. Let $a, c$ be positive constants, for each real number $t$, let $\left(x_{1}, y_{t}\right)$ be the coordinates of the vertex of the parabola $y=a x^{2}+t x+c$. Then, for all real numbers $t$, the figure formed by the vertices $\left(x_{t}, y_{t}\right)$ on the plane is
A. a straight line
B. a parabola
C. part of a parabola
D. one branch of a hyperbola
4. B Hint: $y=a x^{2}+t x+c$ is a family of parabolas, and $x_{t}=-\frac{t}{2 a}, y_{t}=c-\frac{t^{2}}{4 a}$. Converting to the general equation, we have $y_{t}=$ $-a x_{t}^{2}+c$, the vertex lies on the parabola $y=-a x^{2}+c$.