Question

How do I find function equations and graph those equations on a graph?

Answer 1

@Hoslos

Answer 2

This is an example of what I am asking.

Answer 3

Let me start by how to find equation, given the graph:
One of the ways is to find the following in the graph:
- The values cutting the x-axis
- Any other point, which can also involve cutting the y-axis.

Answer 4

Taking your graph,
- the x values are: -2 and 2
- Any other point: (0,1)
The general formula to use is \[y=a(x-x_{1})(x-x _{2})\], where x1 and x2 are the x-values found. It does not matter which one comes first.
Secondly, the any other point will be replaced in y and x, respectively.
As you can see, the x appears twice and from the point, x=0 and y=1
\[1=a[0-(-2)](0-2)\]. You have everything except for a. That is what we have to find. The constant in this case.
\[1=-4a\]\[a=-\frac{ 1 }{ 4 }\]
Having found the constant, we rewrite the general formula, but now replacing only a and x1 and x2, finalizing the step

\[y=a(x-x _{1})(x-x _{2})\]
\[y=-\frac{ 1 }{ 4 }(x+2)(x-2)\]
\[y=-\frac{ 1 }{ 4 }(x ^{2}-2x+2x-4)\]
\[y=-\frac{ 1 }{ 4 }x ^{2} + 1\]
There is the formula, basing from a point of the curve and the x values.

Answer 5

There is another way of doing this, which is by finding the ''other point'' and the vertex coordinate of the parabola.
The original formula to use is \[y=a(x-p)+q\]
where a is the constant, p and q are x and y values, respectively and y and x are the coordinates of the other point.
The following step is two first replace all the values and you will be left with a to be found.
Once you do that rewrite the formula, by only replacing the values of a, p and q , simplifying your equation.
Unfortunately, this one can be manipulated under this method, because the vertex=other point. They should be different.