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!
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!)
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is it possible that an equation could have more than two points of intersection in a line and parabola
, if so, how?
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!
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how would we know if they wont intersect? is there any way to know that?
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!)
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