What is the the vertex of #y =x^2-6x-7 #?
There are different ways this can be done.
This equation is in standard form, so you can use the formula
Or to save time, you can find the (x) coordinat for the vertex with
Alternatively, you can rearrenge the equation into vertex form:
To do this start by putting a outside the brackets. This is easy because
Now we have to change
To do this we can use the quadratic sentence:
This looks sort of what we need, but we are still far of, as we only have
If we look at
Looking at the right side, we can see it is almost
Another way of doing it would be to make a qualified guess and use the quadratic sentences to see if it is correct.
Now go back to our original formula and replace
This is similar to the vertex form:
When the quadratic equation is in vertex form, the vertex is simply the point
Therefore the vertex is