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What is the minimum possible value for y:

$y = x^2 + 12x + 5$

Feb 26, 2019

#1
+98060
+1

y = x^2 + 12x + 5

In the form    ax^2 + bx + c.....the x value that minimizes y is given by   -b / (2a)

So.....the x value that minimizes y is given by   -12 / (2 * 1)  =  -12 / 2  = -6

Put this into the function and we get that y =   (-6)^2 + 12(-6) + 5 =   36 - 72 + 5 =  -36 + 5  = -31

Feb 26, 2019
edited by CPhill  Feb 26, 2019
#2
+21827
+1

What is the minimum possible value for y:

y = x^2 + 12x + 5

$$\begin{array}{|lrcll|} \hline & y &=& x^2 + 12x + 5 \\ & &=& (x+6)^2 -36+5 \\ & &=& (x+6)^2 -31 \qquad \text{min. if } x = -6 \\ & y &=& 0 -31 \\ & y &=& -31 \\ \hline \end{array}$$

The smallest value of the expression $$y= x^2 + 12x + 5$$ is -31

Feb 26, 2019