Final answer:
A quadratic function in vertex form whose graph has the vertex (1,8) and passes through the point (3,12) is y = (1/2)(x-1)² + 8.
Step-by-step explanation:
To write a quadratic function in vertex form, we can use the formula y = a(x-h)² + k,
Where (h,k) represents the vertex.
In this case, the given vertex is (1,8), so our equation becomes y = a(x-1)² + 8.
Now, we can substitute the coordinates of the other given point (3,12) into the equation to find the value of a.
Plugging in these values, we get 12 = a(3-1)² + 8. Simplifying, we find that 12 = 4a + 8.
By solving this equation, we find that a = 1/2.
Therefore, the quadratic function in vertex form, with a vertex of (1,8) and passing through the point (3,12), is y = (1/2)(x-1)^2 + 8.