How do you find the vertex of #f(x)= -x^2-3x-6#?

1 Answer
Jan 1, 2016

The solution set(or vertex set) is: #S={-3/2,-15/4}#

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)=−triangle/(4a)#

In this case:
#x_(vertex) = - (-3)/(2* (-1)) = - (3/2) = -3/2# and
#y_(vertex) = - ((-3)^2 -4 * (-1) * (-6)) / (4 *(-1))#
#y_(vertex) = - (9 - 24)/ -4 = - (15/4) = -15/4#

So, the solution set(or vertex set) is: #S={-3/2,-15/4}#