The turning point of a parabola is the same as the vertex of the parabola. This means that the coordinate of the turning point is also the coordinate of the vertex. Recall, the vertex form of a quadratic equation is expressed as
y = a(x - h)^2 + k
where
a is the leading coefficient
h and k are the x and y coordinates of the vertex.
From the information given,
Coordinate of turning point or vertex is (2.247,0665). This means that
h = 2.247
k = 0.665
Coordinate of other point is (1.27, 0.32). This means that
x = 1.27
y = 0.32
By substituting these values into the equation, we have
0.32 = a(1.27 - 2.247)^2 + 0.665
0.32 = 0.954529a + 0.665
Substracting 0.665 from both sides, it becomes
0.954529a = 0.32 - 0.665 = - 0.345
Dividing both sides by 0.954529, it becomes
0.954529a/0.954529 = - 0.345/0.954529
a = - 0.361
By substituting these values into the equation, the quadratic equation is
y = - 0.361(x - 2.247)^2 + 0.665