SOLUTION: Determine the coordinates the minimum point from the graph of the quadratic function f(x)=x^2+6x-1

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Question 1183591: Determine the coordinates the minimum point from the graph of the quadratic function
f(x)=x^2+6x-1
Found 3 solutions by MathLover1, MathTherapy, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

to determine the coordinates the minimum point from the graph of the quadratic function, graph it :
+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+x%5E2%2B6x-1%29+

the minimum point is at (-3,-10)

or, find the vertex
f%28x%29=x%5E2%2B6x-1.......write in vertex form, complete square
f%28x%29=%28x%5E2%2B6x%2Bb2%29-b%5E2-1........b=6%2F2=3
f%28x%29=%28x%5E2%2B6x%2B3%5E2%29-3%5E2-1
f%28x%29=%28x%2B3%29%5E2-9-1
f%28x%29=%28x%2B3%29%5E2-10=> h=-3, k=-10
the minimum point is at (-3,-10)

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Determine the coordinates the minimum point from the graph of the quadratic function
f(x)=x^2+6x-1
You don't need to Complete the Square in order to find the minimum point.  Unless, of course, you're asked to work the problem by Completing the Square.

You'd need a GRAPHING device to graph the equation, and then use that device to find the vertex.

OR

The minimum occurs where 

       Minimum occurs at

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
Determine the coordinates the minimum point from the graph of the quadratic function
f(x)=x^2+6x-1
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To solve this problem,  literally following its instructions,  you do not need know or apply algebra.

Simply plot the graph and identify the minimum from the graph.