Question

Постройте график функции y=(x+4)²+3

Answer 1

Как-то так. Надеюсь, что понятно.

Answer 2

Graph of the Function y=(x+4)²+3

To graph the function y=(x+4)²+3, we can start by identifying the key features of the equation.

The equation is in the form of a quadratic function, where the variable x is squared. The vertex form of a quadratic function is given by y = a(x-h)² + k, where (h, k) represents the coordinates of the vertex. In this case, the vertex is (-4, 3).

The coefficient a determines the shape of the parabola. Since a is positive in this equation, the parabola opens upwards.

To plot the graph, we can choose a few x-values, calculate the corresponding y-values using the equation, and then plot the points on a coordinate plane.

Let's choose some x-values and calculate the corresponding y-values:

- When x = -6, y = (-6+4)²+3 = 2²+3 = 4+3 = 7 - When x = -5, y = (-5+4)²+3 = 1²+3 = 1+3 = 4 - When x = -4, y = (-4+4)²+3 = 0²+3 = 0+3 = 3 - When x = -3, y = (-3+4)²+3 = 1²+3 = 1+3 = 4 - When x = -2, y = (-2+4)²+3 = 2²+3 = 4+3 = 7

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

| x | y | |---|---| | -6 | 7 | | -5 | 4 | | -4 | 3 | | -3 | 4 | | -2 | 7 |

We can connect these points to form a smooth curve. The resulting graph is a U-shaped parabola that opens upwards, with the vertex at (-4, 3).

Graph of y=(x+4)²+3:


Please note that the graph is a visual representation of the function and may not be to scale.