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

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the vertex for the graph of the quadratic function. f(x) = x^2 - 11      Log On


   

Question 157131: Find the vertex for the graph of the quadratic function.
f(x) = x^2 - 11
Answer by Alan3354(69443) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-11+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A1%2A-11=44.

Discriminant d=44 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+44+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+44+%29%29%2F2%5C1+=+3.3166247903554
x%5B2%5D+=+%28-%280%29-sqrt%28+44+%29%29%2F2%5C1+=+-3.3166247903554

Quadratic expression 1x%5E2%2B0x%2B-11 can be factored:
1x%5E2%2B0x%2B-11+=+%28x-3.3166247903554%29%2A%28x--3.3166247903554%29
Again, the answer is: 3.3166247903554, -3.3166247903554. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-11+%29