Answer:
f(x) = 2(x-5)²-2
Step-by-step explanation:
The equation of a parabola in vertex form is y=a(x-h)²+k where (h,k) is the vertex and "a" represents how stretched or compressed the parabola is and what direction it travels.
Given a vertex of (5,-2) the equation so far is y=a(x-5)²-2
Since we want the parabola to pass through the point (3,6) we must find a value of "a" that satisfies this:
y=a(x-5)²-2
6=a(3-5)²-2
6=a(-2)²-2
6=4a-2
8=4a
2=a
This means that the quadratic function is f(x) = 2(x-5)²-2
