How can you tell if a graph has a positive discriminant?

Question

anonymous · Answer

You're weird... @MasterKush

anonymous · Answer

Do you maybe have an example @touseii45, I find it a bit hard to understand what you're referring to.

anonymous · Answer

anyway, if the grapgh touches  the x axis in two places, the discriminant is positive

anonymous · Answer

attachment

anonymous · Answer

So like with a graph like that it has a positive discriminant?

anonymous · Answer

You have two solutions $x_1$ and $x_2$ here for $$ \Large f(x)=0$$
Such that $f(x_1)=0$ and $f(x_2)=0$ 

So the discriminant must be positive, because the solution formula for the quadratic equation can only compute two solutions if the discriminant is positive.

anonymous · Answer

$$b^2 - 4ac > 0$$  ??????

anonymous · Answer

@Luis_Rivera what about a graph like this?

anonymous · Answer

it touches the $x$ axis once
that means 
a) there is one zero
b) it is a perfect square
c) the discriminant is 0
d) if the equation is $y=ax^2+bx+c$ the then zero is $-\frac{b}{2a}$