SOLUTION: Find the vertex for the graph of the quadratic function. f(x) = x^2 - 11

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Question 157131: Find the vertex for the graph of the quadratic function.
f(x) = x^2 - 11
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Find the vertex for the graph of the quadratic function.
f(x) = x^2 - 11
-----------------
The vertex will be at the minimum.
To find the minimum, set the 1st derivative to 0.
2x = 0
x = 0
That's the x of the vertex, sub it into the eqn to find y:
y = f(x) = 0 - 11
So it's at (0,-11)
Here's a graph to show it.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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: 3.3166247903554, -3.3166247903554. Here's your graph:
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