Answer
True
Work Step by Step
We can rewrite the curve: $y=x^2 + bx + c = (x+\frac{b}{2})^2 + (c-\frac{b^2}{4})$.
We can achieve this curve by translating $y=x^2$ to the left by $\frac{b}{2}$ units to reach $y = (x+\frac{b}{2})^2$.
We then translate $y = (x+\frac{b}{2})^2$ upwards by $(c-\frac{b^2}{4})$ to reach $y=(x+\frac{b}{2})^2 + (c-\frac{b^2}{4})$.
This, as shown above, is equal to $y = x^2 + bx + c$. Thus, each curve in the family $y=x^2 + bx + c$ is a translation of the graph $y=x^2$.
