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Rewrite y=3x^2+6x−1 in vertex form. And please explain what that is.
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Answer:
Yes, it is a function
Step-by-step explanation:
So here's the the thing what is a function? A function tells you the relationship between two variables. It's like a machine. Why you ask? Well because the thing is that for every input or "x" value, there should be ONLY ONE output or "y" value.
For example, you want to some soda or pop, you have three choices. Pepsi, Mountain Dew, and Grape Fanta. If you pick Pepsi you should get a Pepsi, and same thing for the other choices. Yet, lets say you pick the Grape Fanta, yet you got Lemonade?! That isn't what you wanted! So you can think of that when functions come to mind.
Anyways, the question of this problem is to determine if the information we are given is even a function. Well let's see.
Input(s): 2 4 5 8
Output(s): 5 8 6 4
You may be wondering no this isn't a function, but guess what? It is! Why though? Because look at the inputs and outputs! When you put "2" in the machine, you get a "5", pick "4" received an "8", "5" for "6" and "8" and get a "4". Imagine this on a graph, more like coordinate points.
Do any overlap? Do they have the SAME "x" values or "y" values? Nope. If it wasn't a function the inputs would have the same value of output and vice versa.
Overall this is an function. You can determine if a function is a function by graphing the coordinate, placing them in a table to see if they only have one output for each different input, or you can use a the vertical line test. The vertical line test is where you take a pencil hold it up straight and see if there is only one point on the graph for each "x" value.
Overall I hope this made it clear if not please don't be afraid to ask questions or even comment! I hope you have a great day and I attached an example of a graph to show how it is an function
