Question

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

Answer 1

Answer:

(-1, 3)

Step-by-step 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

Answer:

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

Step-by-step 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, $h=\frac{-b}{2a}$ and $k=f(h)$, therefore

$h=\frac{6}{-3}=2$ 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).