Vertex's

[aleskidash]

In my study guide notes I am going over it says this:

The vertex of a quadratic equation is its highest or lowest point on a graph.

If a test asks me for a Vertex will I have to provide the highest or lowest, or the highest and the lowest? Is a point a single point on the X axis, or both axis? If it helps, my test will be multiple choice.

 

[tkhunny]

It's a rather horrible defintion unless you have defined "quadratic equation" to mean ONLY y = f(x). Oh, well, let's just go with it.

The highest point on a graph is just that - the point exceeded by no other. In terms of ordered pairs, x- and y- coordiantes, they look like this (a, b). No other point on the graph has a y-coordinate any greater than 'b'.

You should have this information:

If this is a quadratic equation: y = ax^2 + bx + c, then the x-coordiante of the vertex is -b/2a -- Every time! After that, you can simply substitute into the equation to determine the related y-coordinate.

By the way, if you gather up this vertex and that vertex, and maybe another vertex or two, you will have a collection of "vertices", not "vertexes", and certainly not "vertex's". Just a little language lesson for free.

 

[mmm4444bot]

The shape of the graph is called a parabola.

You can google for information pages, like this one, to see pictures.

If the parabola opens upward, then the vertex is the lowest point on the curve.

If the parabola opens downward, then the vertex is the highest point on the curve.

 

[lookagain]

In my study guide notes I am going over it says this:



If a test asks me for a Vertex will I have to provide the highest or lowest,
or the highest and the lowest? Is a point a single point on the X axis, or
both axis? If it helps, my test will be multiple choice.

aleskidash,

there are also parabolas which are sideways (their axes of symmetry are parallel
to the x-axis), and certain ones whose axes of symmetry are oblique.
Then the "highest point" or the "lowest point" will not apply.