How do you find the vertex of #y= x^2 - 16x + 73#?
Use the equation of a vertex:
If you have a quadratic equation
For your equation,
Thus we know the vertex has an x-coordinate of 8.
To find the y-coordinate, just plug in the x-coordinate back into the function:
So our vertex has a y-coordinate of 9. Therefore our vertex is
An alternate way to approach this is to first put the equation into vertex form. See below for more:
The general form for the vertex form is:
And we get there by completing the square:
We take the
Notice that we can take the first 3 terms and write it as a quantity squared:
and we can simplify the other two terms:
With this form, the vertex is given as