To solve the problem, we will follow the steps outlined:

Given:

We have three points $(1, 7)$, $(2, 10)$, and $(3, 11)$ that lie on a quadratic model of the form $y = ax^2 + bx + c$.

(a) Construct three equations in terms of $a$, $b$, and $c$.

Substitute each point into the equation $y = ax^2 + bx + c$:

1. For the point $(1, 7)$: $7 = a(1)^2 + b(1) + c \implies a + b + c = 7$

2. For the point $(2, 10)$: $10 = a(2)^2 + b(2) + c \implies 4a + 2b + c = 10$

3. For the point $(3, 11)$: $11 = a(3)^2 + b(3) + c \implies 9a + 3b + c = 11$

(b) Use technology to find $a$, $b$, and $c$.

We have the following system of equations: