SOLUTION: Hello my name is Taylor Anne and im a bit confused about how to solve and Quadratic Function. I have a math sheet to do that is titled Transformations: More Than Meets the Eye. f

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Question 292718: Hello my name is Taylor Anne and im a bit confused about how to solve and Quadratic Function. I have a math sheet to do that is titled Transformations: More Than Meets the Eye.
for the instructions it says
Give an example of a function that would fit the following transformations(s) of the quadratic parent function.
my current question that i do not fully understand is
8.The graph of a parabola that is vertically compressed.
see my predicament??? Anyway i would appreciate it if you could help me. Thank you tons in advance
ps: could you also include how to do this step by step and also a few bits of termenology that i need help comprehending like "vertically stretched"
and also whats the difference between domain and range and dependent and independent variables.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
When they say that a graph is "vertically compressed", they mean that the graph has been "squished" (vertically).

Take the standard function (which is graphed below)

and simply "squish" the graph vertically. In other words, imagine pressing something really heavy on the entire graph to get something like this

Above is the graph of (red) and the graph of (the green vertically "squished" graph)

Note: "vertically stretched" is the opposite of "vertically compressed". Ie "vertically stretched" pulls the graph out in the y direction while "vertically compressed" squeezes the graph in the y direction.

As for the other questions...

Domain: The set of all allowable inputs. This is simply the collection of all numbers that you are allowed to plug into a function. You can think of this set as the set of all possible 'x' values to plug in.

Range: The set of all possible outputs. This is the collection of all numbers that are produced when you plug in each value from the domain. You can think of this set as the set of all possible 'y' values that pop out of the function.

Independent Variable: This variable is allowed to take on any value that is in the domain. It does not change due to another variable. The independent variable is often denoted as 'x'.

Dependent Variable: This variable depends on the independent variable. In other words, its value will change if the independent variable. However, it is not the other way around. The dependent variable is often referred to as 'y'.

These definitions are just summaries as there is a lot more to them.