Answer:
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
