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.