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

May 12, 2015

From the formula $y = \left(\frac{1}{2}\right) \left(x + 1\right) \left(x - 5\right)$, 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 $x = \frac{- 1 + 5}{2} = 2$.

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

$y = \left(\frac{1}{2}\right) \left(2 + 1\right) \left(2 - 5\right) = \left(\frac{1}{2}\right) 3 \left(- 3\right) = - \frac{9}{2} = - 4.5$

So the vertex of the parabola is at $\left(2 , - 4.5\right)$.

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.