We are given the following functions:
[tex]\begin{gathered} I\mathrm{}y=8x^2-3x-7 \\ \text{II. y=}6-2x^2 \\ \text{III. y=}2x+4x^2 \\ IV\text{. y=}-x^2+5x+117 \end{gathered}[/tex]
All the functions are of the form:
[tex]y=ax^2+bx+c[/tex]
Therefore, they represent parabolas. A parabola has a maximum when it opens downwards, and a parabola opens downwards if:
[tex]a<0[/tex]
This means, that when the coefficient of the variable squared is negative, then the function has a maximum.
For the given functions, the ones that have a maximum would be II and IV. Therefore, the right answer is A.
