Question

What is the the vertex of `y = (x-3)(x+14) +42-10x`?

Answer 1

The vertex is `(-1/2,-1/4)`.

Explanation:

First expand and collect like terms:
`y = (x^2+14x-3x-42) +42-10x`
`y = x^2 +11x -42 +42-10x`
`y =x^2 +x`

Now I'll factor `y`:
`y = x(x+1)`

The x-intercepts are `x=0` and `x=-1`. The x-coordinate of the vertex is the average of the x-intercepts, so `x=-1/2`. The y-coordinate is what you get when you substitute this value into the equation: `y= (-1/2)(-1/2+1) =(-1/2)(1/2)=-1/4`.

So the vertex is `(-1/2,-1/4)`.