Sorry, I cannot draw a graph as I am a language model. However, I can provide an explanation on how to sketch the graph of the polynomial x2 + 2x + 4:
To sketch the graph of the polynomial x2 + 2x + 4, you can use the following steps:
1. Find the coordinates of the vertex:
The vertex of the parabola defined by x2 + 2x + 4 is located at the point (-b/2a, f(-b/2a)), where a = 1, b = 2, and c = 4. Therefore, the vertex is at (-1, 3).
2. Find the y-intercept:
The y-intercept is the value of the polynomial when x = 0. In this case, when x = 0, y = 4. Therefore, the y-intercept is at (0, 4).
3. Find the x-intercepts:
The x-intercepts are the values of x when y = 0. To find them, you can use the quadratic formula or factor the polynomial. In this case, the polynomial cannot be factored, so you can use the quadratic formula:
x = (-b ± sqrt(b2 -4ac)) / 2a
x = (-2 ± sqrt(4 - 16)) / 2
x = -1 ± sqrt(3)i
Therefore, the polynomial has no real x-intercepts.
4. Sketch the graph:
Using the information from steps 1-3, you can sketch the graph of the polynomial x2 + 2x + 4. Since the vertex is at (-1,3) and the parabola opens upward, the graph will look like a U-shape. The y-intercept is at (0,4). Since there are no real x-intercepts, the graph does not cross the x-axis.
I hope this helps!
Draw the model to represent the polynomial x2 + 2x + 4
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