Final answer:
The equation of the parabola with vertex (6, -3) that passes through the point (8, 5) is y = 2(x - 6)² - 3.
Step-by-step explanation:
To write the equation of the parabola in vertex form when the vertex is given as (6, -3) and the parabola passes through the point (8, 5), we use the vertex form of a parabola's equation, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola. In this case, we already have the vertex (6, -3), so our equation will start as y = a(x - 6)² - 3.
Next, we can use the point (8, 5) that lies on the parabola to find 'a'. Plugging the point into the vertex form, we get 5 = a(8 - 6)² - 3. Simplifying this, we get 5 = 4a - 3. Solving for 'a', we find that a = 2.
So, the equation of the parabola in vertex form is y = 2(x - 6)² - 3.