# How do you graph f(x) = -(x-2)(x + 5)?

Aug 1, 2018

There are quite a number of tools we can use to graph functions.

First, we know this is a polynomial. We also can see that it is degree two, since there are two first degree terms (and if we multiplied it through we would get ${x}^{2}$ but nothing higher).

Now that we know it is second degree, we know that means it could be a concave or a convex parabola. That is determined by the sign of the coefficient of ${x}^{2}$, i.e. if the number before ${x}^{2}$ is positive or negative. We can see pretty easily that the coefficient will be $- 1$, so it will be a convex parabola, i.e. going down.

From here, this equation is factored. This means that we can easily see what the zeros are. They happen when $x - 2 = 0$ or $x + 5 = 0$, i.e. $x \in \left\{- 5 , 2\right\}$.

Now that we know all of this, we can plot the function. The function goes up to $x = - 5$ and then in between it maxes out and then it falls down, through $x = 2$ and down to infinity. This should resemble this
graph{-(x-2)(x+5) [-8, 8, -10, 20]}