SOLUTION: Please help with the following problem. Consider the function f(x)=x^2+6x-2. Find h, the x-coordinate of the vertex of this parabola.

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Question 164879: Please help with the following problem. Consider the function f(x)=x^2+6x-2. Find h, the x-coordinate of the vertex of this parabola.
Found 2 solutions by jim_thompson5910, KnightOwlTutor:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
For any quadratic , the x-coordinate of the vertex can be found by the formula

From we can see that , and

Plug in and

Multiply

Reduce

So the x-coordinate of the vertex is

Answer by KnightOwlTutor(293) (Show Source):
You can put this solution on YOUR website!
You first have to complete the square.
0=x^2+6x-2
Add 2 to both sides
2=x^2+6x
Take the 6 and half it. Then take the value in this case it is 3 and square it.add 9 to both sides.
2+9=(x+3)^2
0=(x+3)^2-11
The vertex is at (3,-11)

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=44 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.3166247903554, -6.3166247903554. Here's your graph: