Pls me get the answer and me understand how to solve these type of questions

y = (x - 4)² + 2

Step-by-step 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