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

1 Answer
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 {-5, 2}#.

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]}