A quadratic function is any function that can be written in the form , where a, b ,and c=R and a didn’t =0.

This is called the general form of the equation of a quadratic function.

The graph of ever quadratic function is a curve called a parabola.

The vertex of a parabola is its highest or lowest point . the vertex may be a minimum point or a maximum point.

The axis of symmetry intersects the parabola at the vertex.The parabola is symmetrical about this line.

The X-intercept is mean the points that when the parabola touch the horizontal line and the Y-intercept is mean the points that when the parabola touch the vertical line.

Analyzing quadratic functions of the form:

is the parents function,

The vertex is (0,0)， X-intercept is (0,0),Y-Intercept is (0,0)

We learned a new one:

This R is a positive number, if this number change to the more and more big, it will make the parents function goes up (+R),and the vertex goes up too.

The second one is :

This R is a positive number,if this number change to the more and more small, it will make the parents function goes down(-R),and the vertex goes down too.

The third one is , |a|>0

when |a|>1, the parabola will be more and more skinnier with the ‘a’number goes more and more big,

when |a|<1,the parabola will be more and more compression with the number goes more and more small.

WARN: If the “a” is a negative number the parabola opens down, if the “a “is a positive number , the parabola opens up

The fourth function is

The R is a positive number, so the size of this number is the distance to the left the parents function

The fifth function is

The R is a negative number, the size of this number is the distance to the right the parents function

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