The quadratic function in vertex form of a parabola vertex 1,1 and passes through 4,19

y = 2 (x - 1) ² + 1

Step-by-step explanation:

The equation of a quadratic function 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) = (1, 1), thus

y = a (x - 1) ² + 1

To find a substitute (4, 19) into the equation

19 = a (4 - 1) ² + 1

19 = 9a + 1 (subtract 1 from both sides)

18 = 9a (divide both sides by 9), thus

a = 2

y = 2 (x - 1) ² + 1 ← in vertex form