Respuesta :
In the equation:
[tex]y=-3x^2-12x-8[/tex]the leading coefficient, a, is equal to -3. Given that a is less than zero, then the parabola has the shape of a ∩. Therefore, it has a maximum.
To find the maximum, we need to find the vertex (h, k) of the parabola.
The x-coordinate, h, is found as follows:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{-(-12)}{2\cdot(-3)} \\ h=\frac{12}{(-6)} \\ h=-2 \end{gathered}[/tex]The y-coordinate, k, is found substituting the value of h into the equation of the parabola, as follows:
[tex]\begin{gathered} k=-3h^2-12h-8 \\ k=-3\cdot(-2)^2-12\cdot(-2)-8 \\ k=-3\cdot4+24-8 \\ k=4 \end{gathered}[/tex]Then, the maximum is placed at (-2, 4)
