Which equation is y = 2x2 – 8x + 9 rewritten in vertex form?

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

 

The formula would be (x + 6)^2 + (y - 5)^2 = 81.

This is the equation for a circle. We added plus 6 to the x term to get it to move to the left. And we add minus 5 to the y term to get it to move up 5 units.