There are different ways to represent a polynomial, but a common model is a graph. To draw the graph of the polynomial x^2+2x+4, we can follow these steps:
1. Choose some x values that span the range of interest. For example, we could pick x=-3, -2, -1, 0, 1, 2, 3.
2. Plug each x value into the polynomial to get the corresponding y value. For example, for x=1, y=1^2+2(1)+4=7.
3. Plot the points (x,y) on a labeled coordinate system with x and y axes. For example, (-3,13),( -2,8), (-1,5), (0, 4), (1, 7), (2, 12), (3, 19).
4. Connect the points with a smooth curve.
The resulting graph should look like a parabola opening upwards, with its vertex at (-1,-1) and its axis of symmetry parallel to the y axis. The coefficients of the polynomial determine the shape, position, and orientation of the curve.
Draw a model to represent the polynomial x2+2x+4.
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