What is the vertex form of y= 5x^2 + 5x -12 y=5x2+5x−12?

1 Answer
Ahmemaru
Mar 5, 2018

vertex = (-1/2, -13.25)vertex=(−12,−13.25)

Explanation:

y = 5x^2 + 5x - 12y=5x2+5x−12

take 5 as a common factor from the first two terms

y = 5(x^2 + x) - 12y=5(x2+x)−12

completing square

y = 5(x^2 + x + (1/2)^2) - 12 -5/4y=5(x2+x+(12)2)−12−54

for completing square you take half the coefficient of x and square it
and we subtract 5/4 because from completing square we get 1/4 so 1/4 times 5 is 5/4 because it is positive inside it must be negative then

y = 5(x+1/2)^2 - 13.25y=5(x+12)2−13.25

from the law y = (x - h)^2 + ky=(x−h)2+k

the vertex is = (-1/2, -13.25)(−12,−13.25)

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