Alg. 1: 9.5 - Finding Intersections of Parabolas

How to algebraically find the intersection points between a parabola and a line, as well as between two parabolas.

[@ASkruger]

You are a chad, a lifesaver, and the world is blessed to have you. Thank you sir.

[@sohrabaziz1478]

I legit cannot thank you enough

[@jawadhindi646]

Nice work. Thank you

[@the.r32]

Great, thank you

[@inderjotsingh1520]

Thank you

[@user-uc5fs7qe3l]

is it possible that an equation could have more than two points of intersection in a line and parabola , if so, how?

[@mr.murraysmathland381]

If you're finding the intersection of a line and a parabola, or a parabola and a parabola, there can be 0, 1, or 2 points of intersection. If you're finding the intersection of higher degree functions, such as x^3, x^4, etc., the graphs can have more curves, and thus, you can have more points of intersection! Try playing around with graphs on Desmos to see!

[@roshinirose8119]

how would we know if they wont intersect? is there any way to know that?

[@mr.murraysmathland381]

Yes; if you do the Quadratic Formula, and the portion inside of the square root ( b^2 - 4ac...called 'the discriminant') is negative, there will be no real solution since the square root of a negative number does not exist. This means the two graphs do not intersect! (This type of solution is called 'imaginary', which comes up a lot in Algebra 2 and beyond!)

[@xander1201]

your voice is chadlike

[@user-ez7kd6xq1w]

Thank you