Question

Find the vertex for the parabola given by the function ƒ(x) = −3x2 − 6x.

Answer 1

(-1, 3)

Explanation:

To find the vertex, we first find the axis of symmetry To do this, we use the equation

x = -b/2a

In our equation, the value of a is -3; the value of b is -6; and the value of c is 0. Using these in the equation for the axis of symmetry, we have

x = -(-6)/2(-3) = 6/-6 = -1

Next we plug this back into our function:

f(-1) = -3(-1)²-6(-1) = -3(1)--6 = -3+6 = 3

This makes the vertex (-1, 3).

Answer 2

The vertex of the parabola is (-2,0)

Explanation:

The given function is:

`f(x)=-3x^(2)-6x`

Now, in order to find the vertex for the parabola, that is v(h,k), comparing the above equation with the standard form of equation that is
`f(x)=ax^(2)+bx+c`, we get

a=-3, b=-6 and c=0

We know,
`h=(-b)/(2a)` and
`k=f(h)`, therefore

`h=(6)/(-3)=2` and
`f(h)=f(-2)=-3(-2)^(2)-6(-2)`

`f(h)=-3(4)+12=-12+12=0`

Thus, the vertex is given as:(h,k)=(-2,0).