We will determine a quadratic function in vertex form:
y = a ( x - 4 )² + 2
4 = a ( 5 - 4 )² + 2
4 = a + 2
a = 2
y = 2 ( x - 4 )² + 2
Then we will determine a linear function in standard form, that passes through the points ( -3, 7 ) and ( 8, 2 ).
7 = -3 m + b
2 = 8 m + b / ·(-1)
----------------------------
7 = - 3 m + b
+
- 2 = - 8 m - b
---------------------
5 = - 11 m
m = -5/11, 2 = -5/11 · 8 + b, b= 2 + 40/11, b = 62/11
y = - 5/11 x + 62/11 / ·11
11 y = - 5 x + 62
5 x + 11 y = 62
Finally the system of equations is:
y = 2 ( x - 4 )² + 2
5 x + 11 y = 62
