Starter 1 identify each graph Identify the graph

Starter 1 identify each graph Identify the graph, each y -8 8 is a quadratic with single x 2 y 25 x 10 x 5 -64 Each is a quadratic with single x 2 y y 18 -7 x -5 2 9 x

Starter 2 identify each graph Identify the graph, each 16 y -4 4 2 is a quadratic with single x y x 0 10 Each is a quadratic with single x 2 y y 31 36 6 x -5 -4 9 x x

C 1: Graphs 1 a • KUS objectives BAT know and use the six types of transformations to graphs Starter:

Introduction Y = f(x) is any function or equation of a graph. This example is an cubic function/equation. y = f(x) There are six basic types of transformation of a graph i. e. six ways we can move the graph or change its shape

Transf 1 y = f(x) + a y = f(x) +a Point (x, y) becomes point (x, y+a) y = f(x) + a This is a ‘shift’ in the y-direction

Transf 2 y = f(x) y = f(x+a) -a Point (x, y) becomes point (x-a, y) y = f(x+a) This is a ‘shift’ in the x-direction, opposite to the sign of number a

WB 1 Include any intersections and The minimum point

Include the image of points A and B A (-2, 8) B (4, 0)

Transf 3 y = Af(x) y = f(x) Notice what happens at the zeros y = Af(x) This is a ‘stretch’ in the y-direction, Scale factor A. Every answer (y-coordinate) gets multiplied by A

Transf 4 Notice what happens at the y-intercept y = f(Ax) This is a ‘stretch’ in the x-direction, Scale factor 1/A Every x coordinate gets multiplied by 1/A, y values stay the same

Include the image of points A and B A (-3, 9) B (6, 0)

Include the image of points A, B and C A (-5, 7) B (0, 3) C (4, -2)

Transf 5 y = f(x) y = -f(x) This is a ‘reflection’ in the axis, mirror line y = 0 Every y coordinate gets multiplied by -1

Transf 6 Notice what happens at the y-intercept y = f(-x) This is a ‘reflection’ in the y-axis, Every x value gets multiplied by -1, So y values are swapped around

Include the image of points A, B and C B (3, 5) C (9, 0) A (-4, -2)

WB 6 Describe these transformations

KUS objectives BAT know and use the six types of transformations to graphs self-assess One thing learned is – One thing to improve is –

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