Question

How do I use the vertex formula to determine the vertex of the graph for `y = -4x^2 + 8x`?

Answer 1

The vertex of graph of `y=ax^2+bx+c`

has `x`-coordinate `x=-b/(2a)`

So, the `x`-coordinate of the vertex of the graph of `y=-4x^2+8x` is:

`x= -(8)/(2(-4)`, which we can evaluate (simplify, calculate)

`x= -(8)/(2(-4)) = -8/-8 = 1`,

To find the `y`-coordinate of the vertex, find the value of `y`, when `x=1`

`y = -4(1)^2 +8(1) = -4 + 8 = 4`

The vertex is: `(1, 4)`.