​Recall The Quadratic Relation

​Linear Relationships have a constant first difference (a constant rate of change)

Qudratic Relations have a constant second difference

​Degree of Polynomial

​The Highest Degree of a linear function (the number in the expoennt) is 1

​y=mx+b

​You can identify a quadratic expression (or second-degree expression) because it’s an expression that has a variable that’s squared and no variables with powers higher than 2 in any of the terms. (The degree is no higher than 2)

The Parabola

When we graph a quadratic relation we see that it creates a special kind of curve known as the parabola

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​One particular form of a quadratic equation is vertex form

​It is useful because it tells you what the vertex of the parabola is without having to do any serious heavy lifting

​Vertex Form

​Stretch / Compression Factor

​The 'a' vbalue of the vertex tells you how stretched or compressed yoru parabola will be

​If a is positive it opens up

​If a is negative it opens down

​The bigger the number of a the more stretched the parabola becomes

​The closer a gets to zero the more compressed the parabola becomes

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​The Step Pattern

​The Step Pattern when a =1 is always 1,3,5

​Anytime you see a different number for a that is essentially the multipier for your step pattern

​Graphing Parabolas

​When graphing parabolas given the vertex form simply mark your vertex and follow the step pattern starting at the vertex

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If you are given the graph of a parabola identify the coordinates of the vertex and then identify the step pattern to find the 'a value'