Question

Find the vertex of y = x2 + 14x − 40 by completing the square. A. (−7, 89) B. (−89, −7) C. (7, 89) D. (−7, −89)

Answer 1

Alright, lets get started.

$y = x^2 + 14 x - 40$

For making complete square, we will add and subtract 49 in this

$y = x^2 + 14 x - 40 + 49 - 49$

$y = x^2 + 14 x + 49 -40 - 49$

$y = (x+7)^2 - 40 - 49$

$y = (x+7)^2 - 89$

Comparing the standard equation of parabola

$y = a (x-h)^2 + k$ where (h,k) are vertex

So, comparing the equation with standard one, h, k would be = (-7 , -89)

So, the vertex are (-7 , -89) : Answer

Hope it will help :)