Dilating trigonometric functions, and quadratic functions are similar. They are, however, not the
same. Compare and contrast the dilations of trigonometric functions and quadratic functions.

Both trigonometric functions and quadratic functions can be dilated vertically and horizontally.

In trigonometric functions, vertical shift, vertical stretch, horizontal stretch and horizontal shift are possible where as in quadratic functions only vertical and horizontal dilation are possible.

Dilation about lines from an axis is possible in quadratic functions dilation.

Step-by-step explanation:

When dilating a trigonometric function, the following applies;

Vertical shift- this is when a graph is moved up or down depending on the value of d. f(x)=trig (x) + dVertical stretch- occurs when a trig function is multiplied by a real number coefficient.In this case, the graph is either dilated or constrict vertically. f(x)= a trig (x)Horizontal stretch -horizontal movements that occur when your change the inside part of the function.It is also called phase shift. f(x)= trig (bx)Horizontal shift-occurs when the inside part of the function is altered to form f(x)= trig (bx+c)The difference between the highest y-vale and the lowest y-value divided by 2 gives the amplitude of the dilated trig graphThe average between the highest y-value and lowest y-value gives the vertical shift.

When dilating a quadratic graph, the following applies;

Vertical dilation-when the parent function is multiplied by a value, it is vertically dilated. a* f(x)Horizontal dilation - when the inputs of a parent functions are multiplied by a value, the parent function is horizontally dilated. if f(x) is the parent function, then multiplied by a, it forms f(a*x) to mean a horizontal dilation of the parent function f(x) by a factor of 1/aA point to note in dilation of quadratic functions is that : some functions can give a similar result when horizontally dilated, vertically dilated or both. For example: y= x² when dilated horizontally by 1/6 then translated horizontally by +2 with no vertical dilation will give a similar graph as that of  y=x² when dilated horizontal by 1/3 , then translated horizontal by +2 .Dilated vertically by a factor of 4. This is a special case to note.