What is the axis of symmetry for f(x) = 2x2 - 4x + 5?
Solution:
Given: f(x) = 2x2 - 4x + 5, let y = 2x2 - 4x + 5
⇒ y = 2[x2 - 2x + 5/2]
⇒ y = 2[x2 - 2x + 1 - 1 + 5/2]
⇒ y = 2(x - 1)2 + 3
⇒ (y - 3) = 2(x - 1)2
⇒ (x - 1)2 = (1/2)(y - 3)
It is of the form (x - h)2 = 4a (y - k) is a parabola whose vertex is at (1, 3)
Therefore, the axis of symmetry is x = 1
What is the axis of symmetry for f(x) = 2x2 - 4x + 5?
Summary:
The axis of symmetry of f(x) = 2x2 - 4x + 5 is x = 1