Final answer:
The coefficient of the shared expression in the parabola's equation is 3.59.
Step-by-step explanation:
The equation of the parabola can be written in the form y = ax² + bx + c. We need to find the coefficient of the shared expression, which is the coefficient of x².
To find the coefficient, we can use the vertex form of a parabola equation: y = a(x - h)² + k, where (h, k) is the vertex. In this case, the vertex is (2, -4), so the equation becomes y = a(x - 2)² - 4.
Now we can substitute the coordinates of the other point (-3, -1) into the equation and solve for a. -1 = a(-3 - 2)² - 4. Simplifying, we get -1 = 25a - 4. Solving for a, we find a = 3.59.