Video: Finding the Roots of a Parabola given Its Graph

Consider the graph: The roots of a quadratic can be read from the graph. What are they?

01:22

Video Transcript

Consider the graph. The roots of a quadratic can be read from the graph. What are they?

Well, to actually be able to answer this question, what we gotta first think about is, well what are the roots of a quadratic? Well, the roots for quadratic are actually when 𝑦 is equal to zero. So what I’ve done is I’ve actually marked that on our graph. And it’s actually the π‘₯-axis cause the π‘₯-axis is where our 𝑦-values are all equal to zero.

If we get back to the question, it says that our roots can be read from the graph. They can be read from the graph because like we said, they are when 𝑦 is equal to zero. So it’s gonna be when the graph actually crosses our line, 𝑦 is equal to zero or the π‘₯ axis. So I’ve actually marked on where these two points are. And we can actually see that our first point is when π‘₯ is equal to negative 0.5. And we can see that our next root is at the point where π‘₯ is equal to negative 1.5.

And therefore, as these are the only two places where our quadratic actually crosses the π‘₯-axis or 𝑦 is equal to zero, we can say: The roots of our quadratic are where π‘₯ is equal to negative a half and π‘₯ is equal to negative three over two.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.