Question 1

coding using r

**[Q1.1] [CODE] Write a function called `parabola` that implements this function.**

$$ f(x) = -x^2 + 2x + 400 $$

```{r} # your code here ```

**[Q1.2] [CODE] Use `curve` to plot the function from $x=-20$ to $x=20$.**

```{r} # your code here ```

**[Q1.3] [CODE] Use `optimize` to find the maximum value of this function, and the value of the function at the maximum.**

```{r} # your code here ```

**[Q1.4] [CODE] Verify your results by calculating the derivative of the function at the maximum value.**

```{r} # your code here ```