Parabolas ​

Notes ​

If we substitute some numbers into

we could make a table to summarise the results:

If we were to plot the values on an $xy$ plane we get a shape called a parabola:

Because this parabola opens upwards (i.e. it is $\cup$ shaped) it is called a convex parabola. A parabola which opens downwards (i.e. it is $\cap$ shaped) is called a concave parabola.

$A$ and $B$ are the roots. At the roots, we have $y=0$, so the parabola cuts across the $x$ axis.

$C$ is the $y$ intercept. This is where the parabola crosses the $y$ axis, meaning $x=0$ at this point.

$D$ is called the vertex of the parabola. The vertex of this parabola is the lowest point because it is convex. If the parabola were concave, the vertex would be the highest point instead.

We're going learn to find some of the key points of parabolas.

Example ​

Exercise ​