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

1 Answer
Ahmemaru
Mar 5, 2018

#vertex = (-1/2, -13.25)#

Explanation:

#y = 5x^2 + 5x - 12#

take 5 as a common factor from the first two terms

#y = 5(x^2 + x) - 12#

completing square

#y = 5(x^2 + x + (1/2)^2) - 12 -5/4#

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 - 13.25#

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

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

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