Translating, reflecting and stretching graphs
Move the graph of y = (x − h)² + k with sliders, read the turning point of a parabola, see where f(2x) sends a point, and combine several transformations on one parabola.
- UK: Year 10
- France: grade 11
- Germany: grade 9
- Iran: grade 12
- Afghanistan: grade 10
- Syria: grade 10
- Palestine: grade 9
- Ukraine: grade 9
- Russia: grade 9
Guide
y = f(x) + k moves the graph up by k (a vertical translation). y = f(x − h) moves it right by h: the sign inside the bracket acts the opposite way, so f(x + 2) moves 2 to the left.
For y = (x − h)2 + k the turning point is at (h, k). Completing the square, x2 − 4x + 1 = (x − 2)2 − 3, gives the turning point (2, −3).
A number multiplying outside (af(x)) stretches the heights, and a negative one turns the graph upside down (a reflection). A number multiplying x inside (f(2x)) acts the opposite way: the graph is squashed in from left and right.