Question

How to graph a parabola `y=1/2(x+1)(x-5)`?

Answer 1

From the formula `y = (1/2)(x+1)(x-5)`, we can tell several things:

The coefficient of `x^2` is positive, so the parabola is upright, shaped a bit like a U.

The parabola crosses the `x`-axis where `y=0`, when `x = -1` and `x = 5`.

The vertex of the parabola will have an `x` coordinate exactly between these two values `x = (-1+5)/2 = 2`.

Substituting `x = 2` into the formula, we get

`y = (1/2)(2+1)(2-5) = (1/2)3(-3) = -9/2 = -4.5`

So the vertex of the parabola is at `(2, -4.5)`.

If you want to know any more points through which the parabola passes, choose an `x` coordinate and substitute it into the formula to get the corresponding `y` value.