What is the vertex form of #y= 9x^2 + 27x + 27 #?

1 Answer
Júlio B.
Jan 1, 2016

The solution set is: #S={-3/2, -27/4}#

Explanation:

The general formula for a quadratic function is:
#y=Ax^2+Bx+C#

To find the vertex, we apply those formulas:
#x_(vertex)=−b/(2a)#
#y_(vertex)=−△/(4a)#

In this case:
#x_(vertex)= -(27/18) = -3/2#

#y_(vertex)= - (27^2 - 4 * 9 * 27)/(4*9)# To make it easier, we factor the multiples of 3, like this:
#y_(vertex)= - ((3^3)^2 - 4 * 3^2 * 3^3)/(4 * 3^2)#
#y_(vertex)= - (3^6 - 4 * 3^5) / (4 * 3^2) = (3^4 * cancel(3^2) -4*3^3*cancel(3^2))/(4 * cancel(3^2))#
#y_(vertex)= - (81 - 108)/4 = -27/4#

So, the solution set is: #S={-3/2, -27/4}#

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