SOLUTION: what is the vertext of f(x)=-x^2+4x+3

Question 715089: what is the vertext of f(x)=-x^2+4x+3

Answer by jsmallt9(3758) (Show Source): 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).
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