Question

Y = - 3x2 – 12x 3x2 – 12x – 8 has a O minimum maximum at Submit Question

Answer 1

In the equation:

`y=-3x^2-12x-8`

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:

`\begin{gathered} h=(-b)/(2a) \\ h=(-(-12))/(2\cdot(-3)) \\ h=(12)/((-6)) \\ h=-2 \end{gathered}`

The y-coordinate, k, is found substituting the value of h into the equation of the parabola, as follows:

`\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}`

Then, the maximum is placed at (-2, 4)