You can put this solution on YOUR website! There are at least two ways to find the vertex of a parabola algebraically. The two that come to mind are...
Complete the square and transform the equation into vertex form.
First I'll rewrite the equation with a y instead of the function notation:
Although not required when completing a square, many people will move the constant term to the other side:
Next we want the coefficient of the squared term to be a 1 so I'll multiply (or divide) both sides by -1:
Next we add the square of half of the coefficient of x to each side. Half of -4 is -2 and -2 squared is 4. So we add 4:
The right side is now a perfect trinomial square. It is (x + (half the coefficient of x))^2:
or, more simply:
With the square completed on the right side there is just one more thing to do: Factor out -1 on the left side:
The equation is now in vertex form, . So we can just read the vertex: (2, 7)
Another way to find the vertex is to memorize and use the fact that when the equation is in standard form, , the x-coordinate of the vertex will be -b/2a. So the x-coordinate of the vertex of will be:
which simplifies to 2.
Then we use this x-coordinate and the equation to find the y-coordinate:
Simplifying...
So the vertex is (2, 7).
(