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Introduction to Parabolas - Concept

Teacher/Instructor Carl Horowitz
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!

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

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.

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