SOLUTION: The function f(x)=x^2-9x+14 has a maximum or minimum value? What is the value?

Question 1033705: The function f(x)=x^2-9x+14 has a maximum or minimum value? What is the value?
Found 3 solutions by josgarithmetic, josmiceli, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Based on so vertex minimum. The vertex occurs in the exact middle of the x-axis intercepts, but does not occur on the axis.

Try finding the vertex putting function into standard form.

This general form indicates that vertex is ( -b/2, c-b^2/4 );

This is .
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

The vertex ( either maximum or minimum )
is at when the form is:

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Another way to see this is: the vertex is midway
between the roots

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The midway point is at:

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Plug this value back into equation

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The vertex is at ( 9/2, -25/4 ), which means it must be
a minimum since there are 2 roots on either side which
are above the vertex.
--------------------
Here's the plot:

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

This quadratic function has the coefficient 1 at . Hence, the parabola is open upward. Memorize it: If the coefficient at is a positive number, then the quadratic function is a parabola open upward and has a minimum. If, in opposite, the coefficient at is a negative number, then the quadratic function is a parabola open downward and has a maximum.

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