Question

Finding the value of `x` given `y` is a maximum? See picture below

Answer 1

When given an equation of the form `y = ax^2+bx+c`, where "a" is negative, the maximum value is the y coordinate of the vertex. The x coordinate of the vertex is:
`h=-b/(2a)`

Explanation:

Given: `y = -16x^2 + 160x - 256`

We observe that `a = -16` and `b = 160`

The x coordinate of the vertex is:

`h = -b/(2a)`

`h = -160/(2(-16))`

`h = 5 larr` this is the answer to [7.a.i]

The maximum value is the function evaluated at `x = h = 5`:

`y = -16(5)^2+160(5)-256`

`y = 144 larr` this is the answer to [7.a.ii]