Question

Постройте график функции y=x^2+2x+4

Answer 1

Графиком функции y=x^2+2x+4 является парабола.
Найдем координаты вершины:
x^2+2x+4
xв=-b/2a
xb=-2/2=-1
yв=(-1)^2-2+4=1-2+4=-1+4=3
(-1;3) - уравнение оси симметрии 

Answer 2

Graph of the Function y = x^2 + 2x + 4

To graph the function y = x^2 + 2x + 4, we can plot several points and connect them to form a curve. Let's start by finding a few points on the graph.

When x = -3: y = (-3)^2 + 2(-3) + 4 = 9 - 6 + 4 = 7

When x = -2: y = (-2)^2 + 2(-2) + 4 = 4 - 4 + 4 = 4

When x = -1: y = (-1)^2 + 2(-1) + 4 = 1 - 2 + 4 = 3

When x = 0: y = (0)^2 + 2(0) + 4 = 0 + 0 + 4 = 4

When x = 1: y = (1)^2 + 2(1) + 4 = 1 + 2 + 4 = 7

When x = 2: y = (2)^2 + 2(2) + 4 = 4 + 4 + 4 = 12

When x = 3: y = (3)^2 + 2(3) + 4 = 9 + 6 + 4 = 19

Now, let's plot these points on a graph:

| x | y | |---|---| | -3 | 7 | | -2 | 4 | | -1 | 3 | | 0 | 4 | | 1 | 7 | | 2 | 12 | | 3 | 19 |

We can now connect these points to form a curve. The graph of the function y = x^2 + 2x + 4 is a parabola that opens upwards. The vertex of the parabola is the point (-1, 3), and the axis of symmetry is the vertical line x = -1.

Please note that the graph provided is a rough sketch and may not be perfectly accurate. It is always recommended to use graphing software or a graphing calculator for precise graphs.

I hope this helps! Let me know if you have any further questions.