Answer:
y = 2(x - 1)² + 7
Explanation:
the equation of a quadratic function in vertex form is
y = a(x - h)² + k
(h, k ) are the coordinates of the vertex and a is a multiplier
given
y = 2x² - 4x + 9
before completing the square, the coefficient of the x² term must be 1
y = 2x² - 4x + 9 ← factor out 2 from the first two terms
= 2(x² - 2x) + 9
to complete the square
add/subtract ( half the coefficient of the x- term)² to x² - 2x
y = 2(x² + 2(- 1)x + 1 - 1) + 9
= 2(x - 1)² + 2(- 1) + 9
= 2(x - 1)² - 2 + 9
= 2(x - 1)² + 7 ← in vertex form