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Equation: y=a(x-h) +k

 

a

  • tells you how narrow or wide the graph is, and whether the graph opens down or up

  • compression-decimal/fraction (wide)

  • stretch-whole number (narrow)

  • opens down, if the (a) is a negative number

  • opens up, if the (a) is a positive number

 

-h

  • tells you where the graph is located on the x-axis

  • this is the axis of symmetry and the x -value of the vertex

  • this lets you know wether the graph is moving left or right (Note: negative h=moving right, positive h=moving left)

 

k

  • tells you where the graph is located on the y-axis

  • this is th optimal value and the y-value of the vertex

  • this lets you know wether the graph is moving up or down (Note: it's not the opposite like -h, so positive k=moving up and negative k=moving down)

 

Quadratic Equations (in vertex form)

Step Pattern

  • the base graph has the step pattern of 1,4,9

  • if the your (a) value is anything other than 1, then multiply it by the step pattern

  • this will give you points, to plot on the graph

For example, your equation might be y=-2(x-3) +4

  • the (a) value for this is -2

  • so, we know that the graph is going to open downwards and the vertex is going to be (3,4)

  • since the (a) value is 2, we are going to multiply 1,4 and 9 by 2

  • so, now the pattern would be 2,8 and 18

*The step pattern tells us the y-value.

*The x-value will always be 1.

*So, you would always go 1 out and however many down/up the step pattern tells you to go.

*Make sure to draw the step patten on both the left and right side of the graph.

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Transformations

  • when writing transformations, they are based on the base graph and go in order of the equation

 

1. Is the (a) value a poitive or a negative?

  • if it's a negative, it reflects the x-axis

  • if it's a positive, you don't write anything

2. Is the (a) value any other number, besides 1?

  • if it's a whole number you write, vertical strech by a factor of___(the number)

  • if it's a decimal/fraction you write, vertical compression by a factor of __(the number)

3. What is the h-value? Is it a postive or negative?

  • if it's negative you write, horizontal shift right ___(value of h) units

  • if it's a positive you write, horizontal shift left ___(value of h) units

4. What is the k-value? Is it a positive or negative?

  • if it's negative you write, vertical shift down___(value of k) units

  • if it's a positive you write, vertical shift up ___(value of k) units

For example, your equation might be y=-2(x-3) +5

  • reflects the x-axis

  • vertical strech by a factor of 2

  • horizontal shift, right 3 units

  • vertical shift, up 5 units

 

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