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42 Cards in this Set
- Front
- Back
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If x2 or y2 is present (but NOT both)
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parabola
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x2+y2=k
ax2+ay2=k |
circle
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ax2+by2=k or by2+ax2=k, a cannot equal b
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ellipse
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ax2-by2=k, by2-ax2=k (a can = b)
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hyperbola
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Inverse variation (i.e. in the form xy=k)
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equilateral hyperbola
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reflect over x-axis
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(x,-y)
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Reflect over y-axis
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(-x, y)
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Reflect over y=x
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(y,x)
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Reflect over y=-x
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(-y,-x)
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Reflect over x=a
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(2a-x, y)
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Reflect over y=b
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(x, 2b-y)
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Reflect through (0,0)
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(-x,-y)
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Rotate 90 degrees with respect to origin
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(-y,x)
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Rotate 180 degrees (origin)
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(-x,-y)
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Rotate 270 degrees (origin)
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(y, -x)
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Ta,b
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(x+a, y+b)
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Dilation of k (origin)
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(kx, ky)
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-y=f(x) or y=-f(x)
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reflect over the x-axis
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y=f(-x)
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reflect over the y-axis
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y=If(x)I (absolute value of
f(x)) |
reflect pieces below the x-axis to above
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y=f(IxI)
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Duplicate right to left (erase left side of graph, and then reflect right side over the y-axis)
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y=f(x-h)
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Translate right h units (h>0)
Translate left h units (h<0) |
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y-k=f(x)
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Translate up k units (k>0)
translate down k units (k<0) |
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y=c*f(x)
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A vertical stretch-multiply y-coordinates only by c (c>1)
A vertical shrink-multiply y-coordinates only by c (0<c<1) |
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y=f(c*x)
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A horizontal shrink-multiply x-coordinates only by 1/c (c>1)
A horizontal stretch-multiply x-coordinates only by 1/c (0<c<1) |
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b2-4ac<0
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2 conjugate, imaginary roots
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b2-4ac=0
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2 rational, equal roots (double-root)
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b2-4ac>0
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2 real, unequal roots
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b2-4ac is a perfect square
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rational roots
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b2-4ac is not a perfect square
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irrational roots
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The composite of two line reflections over parallel lines is a
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translation
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The composite of two intersecting line reflections is a
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rotation
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the composite of two line reflections over perpendicular lines is a
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180 degree rotation (half turn)
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The composite of two line reflections over the same line is the
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identity transformation
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Glide reflection
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a transformation that is the composite of a line reflection and a translation whose direction is parallel to the line reflection
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Isometry
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a transformation that preserves distance
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direct isometry
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isometry that preserves orientation
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opposite isometry
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isometry that reverses orientation
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line reflection (what type of isometry?)
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opposite isometry
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translation
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direct isometry
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rotation (isometry? what type if so?)
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direct isometry
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dilation (isometry?)
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NOT an isometry
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