Question

What is the vertex form of `5y=-x^2 + 9x +8`?

Answer 1

`y=-1/5(x-9/2)^2+113/20`

Explanation:

We need the form of: `y="something"` so divide all of both sides by 5 giving:

`y=-1/5x^2+9/5x+8/5" ".......Equation(1)`

Write as:

`color(green)(y=-1/5(x^2-color(red)(9)x)+8/5)`

Halve the `color(red)(9)` and write as:

`color(green)(y=-1/5(x-color(red)(9)/2)^2+k+8/5)" "....Equation(2)`

The `k` is a correction factor as by doing the above you have added a value that is not in the original equation.

Set `color(green)(-1/5(-color(red)(9)/2)^2 +k=0)`

`=> k=+81/20`

Substitute for `k` in `Equation(2)` giving:

`color(green)(y=-1/5(x-color(red)(9)/2)^2+81/20+8/5)" "....Equation(2_a)`

`y=-1/5(x-9/2)^2+113/20`