Question

PLEASE HELP ASAPPP!! I WILL GIVE BRAINLIEST AND POINTS!!

Answer 1

Step-by-step explanation:

you can arrange f(x) as :

f(x) = 3(x^2 +3x ) +12 = 3 (x +1.5) ^2 + 5.25

so you can see the vertex is at (0,5.25) when x =-1.5

the axis symmetry then lies in x =-1.5

Answer 2

Answer:

The vertex is at (-3, 9).

The axis of symmetry is x = -3.

Step-by-step explanation:

We have the function:

$f(x)=-x^2-6x$

And we want to determine its vertex and the equation of its axis of symmetry.

The vertex can be found with the following formulas:

$\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -1, b = -6, and c = 0.

Find the x-coordinate of the vertex:

$\displaystyle x=-\frac{(-6)}{2(-1)}=-3$

To find the y-coordinate substitute this value back into the function:

$\displaystyle f\left(-\frac{b}{2a}\right)=f(-3)=-(-3)^2-6(-3)=9$

So, the vertex of the equation is (-3, 9).

The axis of symmetry is goes through the vertex point. So, the equation for the axis of symmetry is simply the x-value. Therefore, the equation is:

$x=-3$