f(x) = 1 / 3 x² - 4 / 3 x - 5 / 3
using the form:
f(x) = a(x - h)² + k
The vertex coordinates are 2 and -3.
h = 2
k = - 3
therefore,
f(x) = a(x - 2)² - 3
f(x) = a(x - 2)² - 3
let's use the coordinates (-1, 0) to find a. Therefore,
0 = a(-1 - 2)² - 3
0 = 9a - 3
3 = 9a
a = 3 / 9
a = 1 / 3
let's insert the value of a in the equation.
f(x) = a(x - 2)² - 3
f(x) = 1 / 3 ( x - 2)² - 3
f(x) = 1 / 3 (x - 2)(x -2) - 3
f(x) = 1 / 3 (x² - 4x + 4) - 3
f(x) = x² / 3 - 4x / 3 + 4 / 3 - 3
f(x) = 1 / 3 x² - 4 / 3 x - 5 / 3
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