Answer:
minimum at (2, - 2 )
Step-by-step explanation:
The equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
If a > 0 then the vertex is a minimum
If a < 0 then the vertex is a maximum
Given
f(x) = 2x² - 8x + 6 ← factor out 2 from the first 2 terms
= 2(x² - 4x) + 6
To complete the square
add/ subtract ( half the coefficient of the x- term)² to x² - 4x
f(x) = 2(x² + 2(- 2)x + 4 - 4) + 6
= 2(x - 2)² - 8 + 6
= 2(x - 2)² - 2 ← in vertex form
with vertex = (2, - 2) and a > 0
Thus minimum at (2, - 2 )
