SOLUTION: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x)=x^2-2x-5

Algebra ->  Functions -> SOLUTION: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x)=x^2-2x-5      Log On


   

Question 1046215: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x)=x^2-2x-5
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52790) About Me  (Show Source):
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Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x)=x^2-2x-5
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A quadratic function with a positive leading coefficient has a minimum and has no a maximum.

A quadratic function with a negative leading coefficient has a maximum and has no a minimum.



Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The graph of the quadratic function:



opens upward and has a minimum value if the lead coefficient, is greater than zero, and opens downward and has a maximum value if the lead coefficient is negative.

The value of the independent variable, that produces the minimum or maximum value is . And the actual minimum or maximum value is the value of the function evaluated at . That is to say:



All you have to do is the arithmetic with your given coefficients.

John

My calculator said it, I believe it, that settles it