Question

Y = -2(x + 2)2 Схема графика функции

Answer 1

y= -2(x+2)²  -  парабола, ветви направлены вниз, вершина в точке (-2,0), проходит через точки (0,-8) , (-4,-8) .

Answer 2

To sketch the graph of the function Y = -2(x + 2)^2, you can follow these steps:

Step 1: Identify key points and the vertex.

• The vertex of the parabola is given by the point (-2, 0). This is because when x = -2, the expression (x + 2)^2 becomes 0, and then multiplied by -2 gives us 0 as well.
• The parabola opens downwards because of the negative coefficient (-2) in front of the squared term.

Step 2: Find additional points to sketch the curve.

• Choose a few x-values around the vertex and calculate their corresponding y-values using the given equation.
  • For example, you can use x = -3, -1, 0, and 1.

Step 3: Plot the points and sketch the parabola.

• Plot the vertex (-2, 0) and the additional points you found in Step 2.
• Draw a smooth curve passing through these points.

Step 4: Add arrows to indicate the direction of the parabola.

• Since the parabola opens downwards, you can add arrows below the curve to indicate its direction.

Here's the sketch of the graph:

yamlCopy code
       |    
       |    
       |    
       |    
-------|-------|------
       |   -2   |
       |   -1   |
       |    0   |
       |    1   |
       |    2   |
       |    3   |

Please note that this is a rough sketch and not to scale. The parabola should have a symmetric shape, and the arrows indicate that it opens downwards.