# What's the shape of ax^2+bx+c=0 equation?

What's the shape of ax^2+bx+c=0 equation? I was putting this equation into graph calculators and all of them show me two straight lines. But, what I see in the book is a parabola. Please help me, I'm so confused ...

Note that $ax^2+bx+c=0$ and $y=ax^2+bx+c$ are completely different objects. The former is an equation and the latter is a function.

The quadratic equation $ax^2+bx+c=0$ has two solutions
$x=\frac{-b+\sqrt{b^2-4ac}}{2a}, x=\frac{-b-\sqrt{b^2-4ac}}{2a}$
provided $b^2-4ac>0$. Note that these are equations of two veritical lines. If the equation has only one solution ($b^2-4ac=0$), then $ax^2+bx+c=0$ would represent only one straight line. That's why you are getting two straight lines.

However, if you mean $y=ax^2+bx+c$, then it represents the graph of a parabola.

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