For quadratics, don't try to transform the whole graph, just the vertex Master Trigonometric Graphs: Understand how affects amplitude, period, and shifts. Use Parent Functions: Familiarize yourself with Check Signs: Misinterpreting as a left shift is the most common error. Remember:
For ( y = 3f(2x) ):
. This tells you the graph is horizontally compressed by a factor of , and then shifted left by bab over a end-fraction HKDSE Style Practice Exercises Exercise 1: Vertex and Translation (Paper 1 Style) The vertex of the quadratic graph
A translation of 3 units to the right and 6 units upwards. Question 2: Coordinate Changes A point lies on the curve . Find the new coordinates of under the transformation Horizontal change: means shift left by 3. New Vertical change: means reflect in x-axis (multiply y by -1). New Answer: transformation of graph dse exercise
Thus ( f(x) = x^2 - 4x + 5 ).
Changes made inside the function's argument counter-intuitively affect the -coordinates. The graph moves opposite to the sign. shifts the graph to the left by Horizontal Translation Rightward: shifts the graph to the right by Horizontal Stretching/Compressing: compresses the graph horizontally by a factor of 1k1 over k end-fraction , and stretches it if Reflections Reflections flip the graph across the coordinate axes. Reflection across the x-axis: negates all -values, flipping the graph vertically. Reflection across the y-axis: negates all -values, flipping the graph horizontally. 2. Systematic Workflow for Successive Transformations
Graph: The parabola opens upward with a vertex at (2, 3). For quadratics, don't try to transform the whole
Graph: The parabola opens upward with a vertex at (0, 3).
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Remember "Inside changes opposite, outside changes direct."
Before we dive into the exercise, ensure you have this table memorized. Let the equation of the graph be $y = f(x)$.
