FIRST
We could determine the quadratic equation with the peak point (vertex) and one of the other point. Then submit it to the formula
y = a(x - h)² + k
(h,k) is the vertex, (x,y) is the other point
SECOND
Determine what's given in the question
(h,k) = (3,4)
(x,y) = (5,0)
THIRD
Solve the problem
With the formula above, input the point and calculate a
y = a(x - h)² + k
0 = a(5 - 3)² + 4
0 = 4a + 4
4a + 4 = 0
4a = -4
a = -1
Determine the equation
y = a(x - h)² + k
y = -1(x - 3)² + 4
y = -(x - 3)² + 4
The answer is option d
