Answer:
y = 1(x + (-5))² + 3
Explanation:
The vertex form of the equation for a parabola is ...
... y = a(x -h)² +k
for vertex (h, k).
The value of "a" represents the vertical expansion factor.
Here, the vertex is given as (5, 3), so the equation is ...
... y = a(x -5)² +3
The point (8, 12) is also on the curve, allowing us to find the value of "a". Substituting those values for x, and y, we have ...
... 12 = a(8 -5)² +3
... 9 = 9a . . . . . . . . subtract 3
... 1 = a . . . . . . . . . . divide by 9
In the form required by the problem, the equation is ...
... y = 1·(x + (-5)) + 3