Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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When graphing a quadratic equation, the resulting shape is not a straight line, but instead a shape called a parabola. **Parabolas** vary in direction and shape. The lowest or highest point in a parabola is called a vertex, which lies on the axis of symmetry. If the leading coefficient of the term to the second degree is positive, the parabola faces up. If it is negative, the parabola faces down.

The graph of y equals x squared is, as

you know, called a parabola, okay?

And, basically, what I'm going to do

now is just give you some language

that goes along with that.

The lowest point is called the vertex.

It could also be the highest point if

the parabola is facing the other

direction.

And there is also what's called the axis of symmetry,

which is basically an invisible line

that goes down the center of the

graph. So if you folded it over, it

would actually be symmetric about

that line, okay?

Depending on your teacher or whatnot, you are going

to have to do various levels of precision,

okay? Some teachers just

want to see a vertex in the general

shape. Other teachers want to

see specific points, sometimes three,

sometimes five. So what you

need to do is find a point here and

point here.

The cool thing about the axis of symmetry is if you find

a point on the right side of your

graph, you can always just transpose

it over to the other side. If

you are out two units and up, say, two

units, you know that then you are

out two and up two. If you are out

three and up five, you also know

that you are out three and up five

on the other side.

Using the axis of symmetry could be really helpful

in taking shortcuts in finding

points in order to plot your graph.

Basically the main association

we are going to talk about right now is

your vertex and your axis of symmetry.