SOLUTION: how do you find the minimum and maximum values and the range of a quadratic function?
for example, the given is: {{{ f(x) = x^2 + 2x + 4 }}}
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Question 986496: how do you find the minimum and maximum values and the range of a quadratic function?
for example, the given is:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
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.
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, }\ =\ -1)
.
The minimum (or maximum) value is simply the 
value substituted into the function everywhere you see an . You have to do the arithmetic.
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.
John
My calculator said it, I believe it, that settles it
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