Question

У=(х+3) в квадрате....... построить график

Answer 1

Строим с помощью подстановки.

у=(х+3)в кв

х 0 -9 2 -7

у 9 0 25 2          0=(х+3)в кв                у=(2+3) в кв      2=(х+3)

у=(0+3)в кв       -х=9         |:(-1)          у=25                 -х=9-2

у=3в кв             х=-9                                                    х=-7  

у=9

 

х 0|-9|2 |-7

у 9| 0|25|2

Answer 2

см. вложение:

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Answer 3

Equation and Graph

To solve the equation \(y = (x+3)^2\) and plot its graph, we can start by understanding the equation and then proceed to graphing it.

The equation \(y = (x+3)^2\) represents a parabola. The general form of a parabola is \(y = a(x-h)^2 + k\), where \((h, k)\) is the vertex of the parabola. In this case, the vertex is \((-3, 0)\) and the parabola opens upwards because the coefficient of \(x\) is positive.

Now, let's plot the graph of the equation.

Graph Plotting

```python import matplotlib.pyplot as plt import numpy as np

x = np.linspace(-10, 4, 100) # Generating 100 points between -10 and 4 y = (x + 3) ** 2 # Calculating y for each x

plt.plot(x, y, label='$y = (x+3)^2$') # Plotting the graph plt.scatter(-3, 0, color='red', label='Vertex (-3, 0)') # Marking the vertex plt.axhline(0, color='black',linewidth=0.5) # Adding x-axis plt.axvline(0, color='black',linewidth=0.5) # Adding y-axis plt.xlabel('x') # Labeling x-axis plt.ylabel('y') # Labeling y-axis plt.title('Graph of $y = (x+3)^2$') # Adding title plt.legend() # Showing legend plt.grid(True) # Adding grid plt.show() # Displaying the graph ```

The graph of the equation \(y = (x+3)^2\) is a parabola with its vertex at \((-3, 0)\) and it opens upwards.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.