Answer:
a = 1/2
Step-by-step explanation:
In the equation of the form
y = a(x - h)² + k
The vertex is (h, k). So, we can replace (h, k) with (3, 4) as follows
y = a(x - 3)² + 4
Now, we can use the point (7, 12) to find the value of a, replacing (x, y) = (7, 12) and solving for a, so
12 = a(7 - 3)² + 4
12 = a(4)² + 4
12 = a(16) + 4
12 - 4 = a(16)
8 = a(16)
8/16 = a
1/2 = a
Therefore, the value of a is 1/2.