Answer:
[tex]0[/tex]
Explanation:
Here, we want to get the maximum/minimum value of the given function
The highest power of the function is 2 and that means it is a quadratic function
Given that the leading coefficient is negative, the function does not have a minimum but a maximum value
To get the maximum value (the y-coordinate of the vertex), we use the following formula:
[tex]\begin{gathered} x\text{ = -}\frac{b}{2a} \\ \\ y\text{ = f\lparen x\rparen} \end{gathered}[/tex]
a represents the leading coefficient
b represents the coefficient of x
Substituting the values, we have it that:
[tex]x\text{ = }\frac{\frac{-6}{7}}{2(-1)}\text{ = }\frac{6}{14}\text{ = }\frac{3}{7}[/tex]
We now substitute this value into the original equation
We have this as follows:
[tex]\begin{gathered} -(\frac{3}{7})\placeholder{⬚}^2+(\frac{6}{7})(\frac{3}{7})-\frac{9}{49} \\ \\ =\text{ -}\frac{9}{49}+\frac{18}{49}-\frac{9}{49}\text{ = 0} \end{gathered}[/tex]
