Answer:
The vertex of the parabola is (-2,0)
Step-by-step explanation:
The given function is:
[tex]f(x)=-3x^{2}-6x[/tex]
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 [tex]f(x)=ax^{2}+bx+c[/tex], we get
a=-3, b=-6 and c=0
We know, [tex]h=\frac{-b}{2a}[/tex] and [tex]k=f(h)[/tex], therefore
[tex]h=\frac{6}{-3}=2[/tex] and [tex]f(h)=f(-2)=-3(-2)^{2}-6(-2)[/tex]
[tex]f(h)=-3(4)+12=-12+12=0[/tex]
Thus, the vertex is given as:(h,k)=(-2,0).
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).
