## College Algebra 7th Edition

maximum: $(-\frac{1}{2},\frac{5}{4})$ no minimas
We are given: $f(x)=1-x-x^{2}$ We factor by completing the square: $1-x-x^{2}$ $-x^2-x+1$ $-(x^{2}+x)+1$ $-(x^{2}+x+\displaystyle \frac{1}{4})+1+\frac{1}{4}$ $-(x+\frac{1}{2})^{2}+\frac{5}{4}$ We see that this is a transformed parabola: $x^2$ reflected around the x-axis, moved left $\frac{1}{2}$ units and up $\frac{5}{4}$ units. Thus the maximum would occur at $(-\frac{1}{2},\frac{5}{4})$.