Question

what is the vertex of the graph of this equation y = -3x^2 - 12x - 9 A. (-2,3) B. (2,3) C. (2,-3) D. (-2,-3)

Answer 1

Answer: Option A

Step-by-step explanation:

The graph of a quadratic function is a parabola.

Find the x-coordinate of the vertex of the parabola with:

$x=\frac{-b}{2a}$

In this case:

$b=-12\\a=-3$

Substitute them into the formula. Then:

$x=\frac{-(-12)}{2(-3)}\\\\x=-2$

Now, substitute the $x=-2$ into the quadratic function to find the y-coordinate of the vertex of the parabola.

Finally:

$y = -3x^2 - 12x - 9\\\\y = -3(-2)^2 - 12(-2) - 9\\y=3$

The vertex is: (-2,3)

Answer 2

Answer:

A. (-2,3)

Step-by-step explanation:

You can write a general equation from an quadratic equation that follow:

y=ax^2+bx+c

and you can calculate the vertex (x1,y1) like:

x1=-b/2a

y1=(4ac-b^2)/4a

Then, you have y = -3x^2 - 12x - 9

where:

a=-3

b=-12

c=-9

Now you can calculate the vertex (x1,y1):

x1=-b/2a=-(-12)/(2*-3)=12/-6=-2

y1=(4ac-b^2)/4a)((4*-3*-9)-(-12^2))/(4*-3)=(108-144)/-12=3