This week, we learned all about parabolas. I had no idea what that word meant until we learned it, but now I have a pretty good understanding.

When graphing quadratic equations, the shape that comes up on the graph is called a parabola. A parabola is basically a U shape, with a vertex (the point at the very bottom or top). It is basically a bunch of repeating numbers, mirroring each other.

When graphing a quadratic equation, there are a lot of things we need to find :

Vertex: 

For example the vertex on this graph is (-1.5,3.75) because that is where the parabola stops

Now, there can either be a maximum or minimum vertex, depending on the coefficient in front of the . If the coefficient is positive, then it is a minimum vertex because the parabola opens up (vertex = lowest point). If the coefficient is negative, then it is a maximum vertex because the parabola opens down (vertex = highest point).

In this graph, it is a minimum vertex because the U shape is opening up.

Line of symmetry :
The line of symmetry is the line that divides the two sides of the parabola apart, it is the value of x in the vertex. The example above’s line of symmetry is -1.5

X-intercept and Y-intercept:

The intercept is the numbers where the parabola crosses either the x or y value. Above, there is no x intercept but the y intercept = 6 because that is where the line crosses.

Domain and Range: 
Domain and Range tell us what numbers fit into or work with this parabola and which don’t. Domain is the x values and Range is the y values. With our example, x can be all real numbers while y > or equal to 3.75 because there are no y values lower than that number