9x + 3y = 4 7x + 3y = 20
1 answer:
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Answer:
[Vertex form]
Step-by-step explanation:
Given function:
We need to find the vertex form which is.,
where represents the co-ordinates of vertex.
We apply completing square method to do so.
We have
First of all we make sure that the leading co-efficient is =1.
In order to make the leading co-efficient is =1, we multiply each term with -3.
Isolating and
terms on one side.
Subtracting both sides by 15.
In order to make the right side a perfect square trinomial, we will take half of the co-efficient of term, square it and add it both sides side.
square of half of the co-efficient of term =
Adding 36 to both sides.
Since is a perfect square of
, so, we can write as:
Subtracting 21 to both sides:
Dividing both sides by -3.
[Vertex form]
<em>It's nice of you to offer, but no thanks.</em>
To correctly graph this, you need to set up a simple equation and table of values. Luckily, this equation is dead-simple; I'll define <em>y</em> as the total cost and <em>x</em> as the number of water bottles sold.
Since 1.50$ is the cost for one bottle, multiplying that with your variable that defined the amount of bottles, <em>x</em>, gets you the total, <em>y</em>. Now that we have a basic equation, we can begin plugging in values.
Recall that a function is basically just something that takes in a value and returns another one; in our case, it takes the <em>amount of bottles</em> and returns the <em>total cost. </em>Now, plug in the x-values present on the graph (specifically only whole numbers, since you can't have a half bottle). I can't make a proper table but I'll make do.
x y
--------
0 0
1 1.5
2 3
3 4.5
4 6
5 7.5
-----------
Great, now that you have a table of values all you have to do is plug them into the graph, which I've attached. It's pretty crude since I drew it in mspaint but I'm sure you get the point at this point.
