Answer:
y = 2(x - 3)² + 7
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
Obtain this form using the method of completing the square.
Given
y = 2x² - 12x + 25 ← the coefficient of the x² term must be 1 so factor out 2
y = 2(x² - 6x) + 25
To complete the square
add/ subtract ( half the coefficient of the x- term )² to x² - 6x
y = 2(x² + 2(- 3)x+ 9 - 9) + 25
y = 2(x - 3)² - 18 + 25
y = 2(x - 3)² + 7 ← in vertex form
