Question

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

Answer 1

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}`