Answer:
y = (x - 4)² + 2
Explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (4, 2), thus
y = a(x - 4)² + 2
To find a substitute a point that lies on the curve into the equation
Using the point (2, 6), then
6 = a(2 - 4)² + 2
6 = 4a + 2 ( subtract 2 from both sides )
4 = 4a ( divide both sides by 4 )
a = 1
Hence
y = (x - 4)² + 2 ← equation in vertex form