How do you find the vertex and the intercepts for #G(x) = x ^ 2 - 6#?
1 Answer
Vertex at the point
Explanation:
Let's first have a look at the
Recall that the difference between two squares can be expressed as:
If we consider 6 as:
We can now convert the function to a difference of squares:
Using the Null Factor Law we can now solve for
Therefore
Let's now have a look at the
Consider that for any function,
Therefore, the
Finally, let's have a look at the vertex of the function:
Consider the general form of a parabolic function:
If we compare the equation that you have presented:
We can determine that:
The
The
The constant term is
Therefore, we can use the formula:
to determine the
Substituting the appropriate values into the formula we get:
Substituting this value into the given function, we get:
Therefore, the vertex of the function is present at the point