Question

What is the maximum/minimum value of the function y = -X2 + (6/7) - 9/49?

Answer 1

`0`

Step-by-step 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:

`\begin{gathered} x\text{ = -}(b)/(2a) \\ \\ y\text{ = f\lparen x\rparen} \end{gathered}`

a represents the leading coefficient

b represents the coefficient of x

Substituting the values, we have it that:

`x\text{ = }((-6)/(7))/(2(-1))\text{ = }(6)/(14)\text{ = }(3)/(7)`

We now substitute this value into the original equation

We have this as follows:

`\begin{gathered} -((3)/(7))\placeholder{⬚}^2+((6)/(7))((3)/(7))-(9)/(49) \\ \\ =\text{ -}(9)/(49)+(18)/(49)-(9)/(49)\text{ = 0} \end{gathered}`