Answer:
y = 2(x - 2)² + 1
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
y = 2x² - 8x + 9
Using the method of completing the square
Factor out 2 from the first 2 terms
y = 2(x² - 4x) + 9
add/subtract ( half the coefficient of the x- term )² to x² - 4x
y = 2(x² + 2(- 2)x + 4 - 4) + 9
= 2(x - 2)² - 8 + 9
= 2(x - 2)² + 1 ← in vertex form
