Draw the graphs of following quadratic functions.
(i) `y=x^(2)+x+1" "` (ii) `y=x^(2)-2x-3`
(iii) `y=2+x-x^(2)" "`(iv) `y=x-1-x^(2)`

Explanation

To draw the graphs of the given quadratic functions, we will follow a systematic approach for each function. We will find the vertex, determine the direction of the parabola, and plot key points.

### Step-by-Step Solution

#### (i) For the function \( y = x^2 + x + 1 \)

1. **Identify coefficients**: Here, \( a = 1 \), \( b = 1 \), and \( c = 1 \).
2. **Find the vertex**: The x-coordinate of the vertex is given by \( x = -\frac{b}{2a} = -\frac{1}{2 \cdot 1} = -\frac{1}{2} \).
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