Question

What is the maximum value of `y = - 9x^2 +126x-431` ?

Answer 1

`y_max = 893` at `x_max=7`

Explanation:

The maximum values of a quadratic `y=ax^2 + bx +c` is found at `x=-b/(2a)`

In this example `a=-9` and `b=126`
`:.x_max = (-126)/-18 = 7`

Plugging this back into the original equation gives
`y_max = -9*7^2 +126*7 -431 = 441 + 883 -431`
`y_max = 893`