Transformation of Curves

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Transformation of Curves
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Task A

• Straight Lines

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What do you notice about the lines as the number
in front of the x becomes bigger?

• The gradient of the line increases
• The line becomes steeper

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What do you notice as the number in front of the
x changes?

• The gradient of the line decreases as the number
  in front of the x increases towards zero
• The line becomes less steep as the number in
  front of the x increases towards zero

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More Straight Lines
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What do you notice about these curves? What
effect does the constant have?

• As the positive constant increases, for example
  the 3 in y2x3, the line moves more to the
  left. F(xa) is the translation of of a units
  parallel to the x-axis.
• As the negative constant decreases, for example
  the -4 in y2x-4, the line moves more to the
  right. F(x-a) is the translation of a units
  parallel to the x-axis.

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The general equation of a straight line is ymxc
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Discuss what the significance of m and c is. What
is the equation for the graph below? Give reasons
for you answer.
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• General equation of line is ymxc
• m refers to the gradient. In this case, the
  gradient is 6 in y6x-4.
• c refers to the y-intercept. In this case, the
  y-intercept is -4.

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Task B

• Quadratics

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A quadratic equation is one that has an x squared
as the highest power. The shape f this is called
a Parabola.
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What do you notice about these curves? What
effect does a negative sign in front of the x
squared?

• As the number before the x squared becomes
  greater, the more stretched the curve becomes in
  the direction of the y-axis. The general
  equation af(x) a stretch parallel to the
  y-axis by scale factor a.
• The negative sign in front of the x squared
  reflects the curve in the x-axis. The general
  equation -f(x) refers to reflection in the
  x-axis.

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More Quadratics
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What effect does adding a different constant have
on the parabola? What is the equation of the
following parabola. Give reasons for answer.

• Adding a different constant to the equation
  causes the parabola to move up and down parallel
  to the y-axis. F(x)a translation of a units
  parallel to the y-axis. F(x)-a is a translation
  of a units parallel to the y-axis.

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• The equation of the parabola is x squared 2.
  The reason being that the parabola is move
  downwards by two units, parallel to the y-axis.

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• F(xa) translation of a units parallel to the
  x-axis.
• F(x-a) translation of a units parallel to the
  x-axis.