Maths - Quadratic and Straight Line Intersections
Pearson Edexcel Mathematics 2022
Finding the intersection
How do you find the intersection for something like $y = 5 - 2x$ and $y = 3x^2 + 5x - 3$?
- Set them equal to each other and simplify.
- $5 - 2x = 3x^2 + 5x - 3$
Number of intersection points
What’s the most amount of times a straight line and a quadratic could intersect?
What’s the least amount of times a straight line and a quadratic could intersect?
Tangency
A line of the form $y = mx+c$ with one point of intersection with a quadratic has what relationship?
That line is a tangent to the parabola.
Why isn’t a straight line with one point of intersection necessarily a tangent?
Consider a straight line like $x = 5$, which passes through a parabola but is not tangent.