document.write( "Question 986496: how do you find the minimum and maximum values and the range of a quadratic function?\r
\n" ); document.write( "\n" ); document.write( "for example, the given is: $\"+f%28x%29+=+x%5E2+%2B+2x+%2B+4+\"$ \n" ); document.write( "

Algebra.Com's Answer #607259 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "The sign on the lead coefficient tells you which way the parabola opens. Positive (like your example) opens up, meaning that the value at the vertex is a minimum. Negative, it opens down, so the value at the vertex is a maximum.\r
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\n" ); document.write( "\n" ); document.write( "The value of

that locates the vertex is given by the opposite of the coefficient on the first degree term divided by twice the lead coefficient. For your problem,

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\n" ); document.write( "\n" ); document.write( "The minimum (or maximum) value is simply the

value substituted into the function everywhere you see an

. You have to do the arithmetic.\r
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\n" ); document.write( "\n" ); document.write( "For a parabola that opens upward, the range is the minimum value to positive infinity. For a parabola that opens downward, the range is minus infinity to the maximum value.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it\r
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