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Parabola with vertical axis vertex (1,1) passing through (0,5)

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Sure, I can help you with that.

The equation of a parabola with a vertical axis and vertex (1,1) is of the form:

```

y = a(x - 1)^2 + 1

```

where `a` is a constant that determines the shape of the parabola.

To find the value of `a`, we can use the point (0,5). Plugging these values into the equation, we get:

```

5 = a(0 - 1)^2 + 1

```

```

5 = 1 + a

```

```

a = 4

```

Therefore, the equation of the parabola is:

```

y = 4(x - 1)^2 + 1

```

To graph the parabola, you can plug in different values of `x` and solve for `y`. For example, if `x = 2`, then `y = 17`.

The parabola will pass through the points (0,5), (1,1), and (2,17).

Here is a Python code that you can use to graph the parabola:

```python

import matplotlib.pyplot as plt

import numpy as np

def parabola(x):

a = 4

return a * (x - 1)**2 + 1

x_values = np.linspace(-2, 3, 100)

y_values = parabola(x_values)

plt.plot(x_values, y_values)

plt.show()

```

This code will create a graph of the parabola. You can run this code by saving it as a Python file and then running it from the command line.

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

User Ageis
by
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