Question 26 (5 points) Determine all points of intersection between the functions $y=x+7$ and $y=x^{2}-4 x+11$. Show all of your work. Complete your work by hand then upload a picture of your work.

Step 1 ：Set the two functions equal to each other: \(x + 7 = x^{2} - 4x + 11\).

Step 2 ：Rearrange the equation to form a quadratic equation: \(x^{2} - 5x + 4 = 0\).

Step 3 ：Solve the quadratic equation for x. The solutions are \(x = 1\) and \(x = 4\).

Step 4 ：Substitute \(x = 1\) into the equation \(y = x + 7\) to find the corresponding y-value. The result is \(y = 8\).

Step 5 ：Substitute \(x = 4\) into the equation \(y = x + 7\) to find the corresponding y-value. The result is \(y = 11\).

Step 6 ：The points of intersection between the functions \(y = x + 7\) and \(y = x^{2} - 4x + 11\) are \(\boxed{(1, 8)}\) and \(\boxed{(4, 11)}\).