# Maths - Quadratic and Straight Line Intersections

> Source: https://ollybritton.com/notes/a-level/maths/topics/quadratic-straight-line-intersections/ · Updated: 2020-09-21 · Tags: maths, school, year-1

##### 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.
* $5 - 2x = 3x^2 + 5x - 3$

##### What's the most amount of times a straight line and a quadratic could intersect??
2.

##### What's the least amoount of times a straight line and a quadratic could intersect??
0.

##### 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 parobala.

##### 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 parobala but is not tangent.

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