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Unit 3 Terms: reflection,vertical shift, horizontal shift, stretch/shrink

Reflection

reflection
Reflection: If there is a negative sign in front of the function, the function flips across the x axis. Transforming Points: Find a point, or some points, on the original graph and multiply the original y coordinate for that point by the negative sign. That gives you the new y coordinate that goes with the original x coordinate. Plot enough transformed points to be able to sketch the transformed function accurately.
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Vertical shift

Vertical Shift: The original graph f(x)=|x| moves up or down by a constant. The constant(number) will be added outside of the function. To draw the transformed graph add the constant to the original y value for a point to get the location of the transformed point. Repeat with more points. Transforming points: Find a point,or some points, on the original function. Add or substract the constant outside the function to the original y coordinate. The transformed points are the original x coordinate and transformed y coordinate.Plot enough transformed points to be able to sketch the transformed function accurately.
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Horizontal shift

If the constant is inside the function (in with the x), the graph will move left or right by the constant in the direction opposite that indicated by the sign. +3 moves the graphed function left 3 units, -3 moves the graphed function right 3 units. Transforming Points: Find a point,or some points, on the original graph. Multiply the constant inside the function by a negative 1, so 3 would be -3. Add that to the original x coordinate to get the transformed x coordinate (so 0 + -3, for instance).The transformed point is the transformed x coordinate with the original y coordinate.
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Stretch/shrink in front of the function

Stretch factor in front of the function:Find a point on the original graph and multiply its y coordinate by the constant(number)to get the y coordinate for the point on the transformed graph. Transforming Points:Find a point,or some points, on the original graphed function. Multiply the original y coordinate times the constant in front of the function to get the transformed y coordinate that goes with the original x coordinate.
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Stretch/shrink in front of the x

Stretch factor inside the function in front of the x:Find a point on the original graph and divide its x coordinate by the constant(number) to get the x coordinate for the point on the transformed graph. Transforming points: Find a point or some points on the original graph. Divide the original x coordinate by two to get the transformed x coordinate that goes with the original y coordinate.
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Practice!

Match quadratic equation with its graph

Hosted by the Scirra Arcade

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Quadratic transformations - move two points

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Halloween Transformations:move the spider to the correct point

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Santa Translated:Get Santa to the correct point

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mathisfun examples and practice problems
khan academy shifts(horizontal and vertical)
khan academy stretch and reflect