Write the quadratic function in the form fx ax h2 k Then

Write the quadratic function in the form f(x) = a(x - h)^2 + k. Then, give the vertex of its graph. f(x) = 3x^2 - 18x + 29 Writing in the form specified: f(x) = Vertex: (,)

Solution

f(x) = 3x^2 -18x +29

= 3(x^2 -6x) +29 taking out 3 as common

= 3(x^2 -6x +9 -9) +29

= 3(x -3)^2 -27 +29

f(x) = 3(x-3)^2 +2

Comparing with standard form we get

Vertex : (3, 2)