Algebra ( Period 5)

Transformations of Quadratic Functions  9-3

Transformations change the position or size of any figure.
In Math 8 we are doing this with geometric figures like triangles and parallelograms. In Algebra we will do this with parabolas.

TRANSLATION:
The parabola stays the same size but simply SLIDES to the left, right, up or down (or even a combination—like up and to the right)

VERTICAL TRANSLATION: A vertical translation up or down happens with you add a constant (k) to a parent function. For example the parent graph y = x² has the vertex at the origin but if you add 4 to the it,
 y = x² + 4à the vertex moves up 4 on the y axis
If you add -4  { y = x² + (-4)  or simply y = x² - 4}  it moves down 4 on the y axis.

HORIZONTAL TRANSLATION: A horizontal translation right or left happens when you add a constant (h) to the  x-value of the parent function.
We place that h value in a ( ) with the x variable:
(x –h)² would be a slide RIGHT

(x + h)² would be a slide LEFT

COMBINATION TRANSLATION: Together, both types of slides are shown by this formula ( known as the VERTEX FORMAT)  f(x) = (x –h)² +k
Notice that since the formula has –h, it moves in the opposite direction right or left. Since the formula is  +k   it moves in the same direction up or down!

DILATION: This type of transformation makes the graph either narrower or wider. As “a” is a smaller and smaller fraction/decimal the parabola gets wider and wider. AS “a” gets bigger—the parabola gets narrower.

REFLECTION: This transformation FLIPS the parabola upside down. This happens when “a” is negative.

So now the full VERTEX FORM of a parabola/quadratic is

y = a(x - h)² + k