SOLUTION: Find the minimum value of the function f(x) = x^2 + 9x – 16.

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Question 1053913: Find the minimum value of the function f(x) = x^2 + 9x – 16.
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
That would be the vertex for this one. Put the function into standard form and read the vertex!

This lesson also will show how, but was written for solving a quadratic equation.

Change from general form to standard form.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Apply completing the square

x^2 + 9x – 16 = %28x+%2B+9%2F2%29%5E2 - %289%2F2%29%5E2 - 16 = %28x%2B4.5%29%5E2 - 81%2F4 - 16 = %28x%2B4.5%29%5E2 - 36.25.


The square term is always positive and get the value of zer0 only at x = -4.5.
Hence, the minimum of the quadratic function is -36.25.

On completing the square to find the minimum/maximum of a quadratic function see the lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
    - A rectangle with a given perimeter which has the maximal area is a square
    - A farmer planning to fence a rectangular garden to enclose the maximal area
    - A farmer planning to fence a rectangular area along the river to enclose the maximal area
    - A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Finding minimum/maximum of quadratic functions ".


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Find the minimum value of the function f(x) = x^2 + 9x – 16.
 Minimum value occurs at: x+=+-+b%2F%282a%29, or at: x+=+-+9%2F2

Minimum value: f%28-+9%2F2%29+=+%28-+9%2F2%29%5E2+%2B+9%28-+9%2F2%29+-+16 ------- Substituting -+9%2F2 for x

Minimum value: f%28-+9%2F2%29+=+81%2F4+-+81%2F2+-+16

Minimum value: f%28-+9%2F2%29+=+81%2F4+-+162%2F4+-+64%2F4

Minimum value: